PENCOYD 


UC-NRLF 


AND 


STEEI 


WILEY  &  SONS 


1 


LIBRARY 


UNIVERSITY   OF   CALIFORNIA. 

Received  .-*^rK><**<*&  188  6. 

Accessions  No.^?'*-*-          Shelf  fib. 


e*- 


-umVVff 

WROUGHT  IRON  AND  -STEEL 


IN 


CONSTRUCTION. 


CONVENIENT    RULES,    FORMULAE,    AND    TABLES  FOR  THB 
STRENGTH     OF    WROUGHT   IRON    SHAPES    USED    AS 
BEAMS,     STRUTS,     SHAFTS,     ETC.,    MANUFAC- 
TURED BY  THE  PENCOYD  IRON  WORKS. 


SECOND  EDITION,  REVISED  AND  ENLARGED. 


THE. 

uim  SRSITT 


>RK. 

JOHN  WILEY  &  SONS, 
15  ASTOE  PLACE, 

1885. 


COPYRIGHT,  1884, 
BT  A.  &  P.  ROBERTS  &  CO. 


PREFACE. 


To  Engineers  and  Builders  in  Iron  and  Steel  this  volume  is 
presented,  with  the  hope  that  it  may  be  of  assistance  to  them  in 
their  daily  labors,  and  afford  information  upon  some  points 
which  have  not  heretofore  been  put  in  published  form.  It  has 
been  the  aim  of  the  author  to  eliminate  as  far  as  possible  mat- 
ters of  theory  from  statements  of  facts,  that,  where  conflict  of 
opinion  may  arise,  each  one  may  draw  his  own  conclusions.  It 
was  considered  advisable  to  treat  only  of  subjects  relating  to 
Iron  and  Steel,  referring  to  any  of  the  numerous  engineers' 
pocket-books  for  information  upon  outside  matters. 

As  far  as  possible,  doubtful  points  were  corroborated  by  ex- 
periments, and  especially  Ihe' article  upon  "Struts  "  is  based 
upon  the  results  of  several  hundred  carefully  conducted  experi- 
ments at  Pencoyd,  for  more  detailed  information  concerning 
which  we  would  refer  to  two  papers  by  Mr.  Jas.  Christie,  pub- 
lished in  the  Transactions  of  the  American  Society  of  Civil  En- 
gineers, entitled,  "  Experiments  on  the  Strength  of  Wrought 
Iron  Struts,"  and,  "  The  Strength  and  Elasticity  of  Structural 
Steel,"  wherein  the  above  experiments  are  fully  described. 
Hereafter  should  errors  be  detected  by  a  more  perfect  knowledge 
of  the  physical  properties  of  the  materials  treated  of,  we  shall 
be  glad  to  acknowledge  the  same,  but  now  offer  the  following 
pages  as  the  best  results  we  are  able  to  obtain  from  present 
practice. 

A.  &  P.  ROBERTS  &  CO. 

PENCOTD,  May,  1884. 


PREFACE  TO  SECOND  EDITION. 


IN  preparing  the  Second  Edition  for  the  press  we  have  cor- 
rected some  small  errors  occurring  in  various  places  in  the  first 
edition,  which  were  discovered  after  its  publication.  A  few  new 
tables  of  weights  of  separators  for  beams,  of  bolts,  nuts  and 
rivets,  which  were  deemed  useful  in  architectural  calculations, 
have  been  added.  Some  additional  shapes  are  described,  and 
several  old  sections  of  beams  and  channels  changed  to  more  effi- 
cient forms,  by  better  distribution  of  material  in  the  flanges. 
At  the  present  writing  we  have  no  alterations  to  make  in  our 
conclusions  in  regard  to  steel,  our  experiments  up  to  date  seem- 
ing to  confirm  our  results  as  then  announced. 

A.  &  £.  ROBERTS  &  CO. 
PENCOYD,  January,  1885. 


PKEFACE  TO  THIRD  EDITION. 


MOKE  than  a  year  has  elapsed  since  the  publication  of  the  first 
edition  of  this  little  volume,  and  we  are  now  preparing  a  third 
for  the  press.  A  few  new  sections  have  been  added  and  several 
errors  overlooked  in  the  earlier  editions  corrected,  so  that  we 
believe  very  few,  if  any,  now  exist.  Our  conclusions  in  regard 
to  struts,  based  upon  Mr.  Christie's  experiments,  have  stood  the 
test  of  publication  and  criticism,  and  we  think  at  this  day  can 
be  said  to  have  more  fully  the  stamp  of  authority  than  when 
first  issued.  We  trust  this  Hand  Book  has  and  will  continue  to 
be  of  value  to  all  who  daily  use  wrought  iron  and  steel  in  con- 
struction. 

A.  &  P.  ROBERTS  &  CO. 

PEKCOYD,  July,  1885. 


CONTENTS. 


PAGES 

TABLES  OF  DIMENSIONS 1-16 

STRENGTH  OF  WROUGHT  IRON 17-23 

STRUCTURAL  STEEL 24-31 

STRENGTH  OF  IRON  BEAMS 32-39 

TABLES  FOR  I  BEAMS 40-45 

TABLES  FOR  CHANNEL  BEAMS 46-49 

TABLES  FOR  DECK  BEAMS 50,  51 

IRON  FLOOR  BEAMS 52-55 

TABLES  FOR  FLOOR  BEAMS 56-62 

BEAMS  SUPPORTING  BRICK  ARCHES  AND 

WALLS 63-66 

APPROXIMATE  FORMULAE  FOR  BEAMS 67-77 

BENDING  MOMENTS  AND  DEFLECTIONS 78-81 

BEAMS  SUPPORTING  IRREGULAR  LOADS 82-84 

BEAMS  SUBJECT  TO  BENDING  AND  COM- 

PRESSION 84-87 

ELEMENTS  OF  STRUCTURAL  SHAPES 87-91 

TABLES  OF  ELEMENTS 92-101 

MOMENTS  OF  INERTIA 102-111 

RADII  OF  GYRATION 112-113 

ROLLED  STRUTS 114-153 

TABLES  OF  I  BEAM  STRUTS 124-134 

"  ANGLE  "  138-140 

"  TEE  "  142,143 

"  CHANNEL  STRUTS 144-153 

COLUMNS..  ..154-159 


VI  CONTENTS. 

PAGES 

EIVETS  AND  PINS 160-162 

STRESSES  IN  FRAMED  STRUCTURES 163-169 

WROUGHT  IRON  SHAFTING 170-177 

PROPERTIES  OF  CIRCLES 178-183 

WEIGHT  OF  ROLLED  IRON 184, 185 

DECIMAL  EQUIVALENTS  FOR  FRACTIONS 186 

ILLUSTRATIONS 

For  a  full  detail  of  the  contents  see  Index. 


UNIVERSITY 


WKOUGHT  IRON  AND  STEEL  IN 
CONSTRUCTION. 


TABLES   OF  DIMENSIONS. 

THE  following  tables  give  the  principal  dimensions  of  the 
standard  shapes  of  structural  iron  and  steel  rolled  at  Pencoyd. 

Further  particulars  of  the  sections  will  be  found  in  the  illus- 
trations at  the  end  of  the  book. 

For  beams  and  channels  the  least  and  greatest  sections  of 
each  size  are  described  in  the  preliminary  tables.  Any  inter- 
mediate sectional  areas  between  the  maximum  and  minimum  can 
be  rolled,  but  the  flanges  remain  unaltered,  the  web  only  being 
thickened.  The  weights  per  yard  corresponding  to  increased 
web  thicknesses  are  given  in  annexed  tables.  For  angles,  any 
thickness  between  the  maximum  and  minimum  can  be  rolled, 
corresponding  weights  for  the  principal  intermediate  thicknesses 
being  given  in  the  tables. 

The  legs  of  angles  increase  slightly  in  width  as  the  thickness 
is  increased.  This  renders  the  actual  weights  corresponding  to 
given  thickness  somewhat  uncertain.  Therefore  either  the  de- 
sired thickness  or  weight  per  yard  should  be  specified,  but  not 
both.  (The  methods  of  altering  the  thickness  of  the  foregoing 
sections,  are  illustrated  in  plate  No.  28.)  The  cross-hatched 
sections  represent  the  least  areas,  and  the  blank  section  the  added 
thickness. 

Tee  sections  cannot  be  altered  from  the  standard  as  given  in 
the  tables.  Flat  bars  can  be  rolled  to  any  thickness  between  the 
limits  given  in  the  list. 


2  WBOUGHT  IKON   AND   STEEL. 

SIZES  OF  MINIMUM  AND  MAXIMUM  SECTIONS. 


PENCOYD 


BEAMS. 


, 

1. 

f. 

1/0 

^ 

1 

1 

a 

B 

q 

•1 

o> 

fl 

^  j 

^| 

Erfs 

o 

ii 
u 

3 

c 

g  ^ 

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5  ^ 

S  " 

P  '—  i 

S^ 

X| 

^ 

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1 

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Jl, 
'5 

—     £-4 

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ll 

F 

II 

M 

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EH 

0) 

6 

55 

* 

i 

*, 

§ 

S 

si 
S 

^ 

A 

B 

B 

c 

C 

D 

E 

i 

2 

15 
15 

200 
145 

233 

201 

i 

y 

5| 

54 

i 

ijL 

f 

312 
412 

168 
120 

194 

1(33 

1! 

A 

5t, 

511 

i 

li 

M 

5 

101 

134 

161 

M 

it 

5L 

5£ 

li- 

fi 

f 

Kt 

108 
89 

135 
109 

8 

If 

3 

Mi 

lt 

M 

S 

7 

10 

112 

137 

* 

1 

4-| 

4] 

IT? 

^ 

8 

10 

90 

106 

M 

4$ 

f^ 

H 

9 

9 

90 

122 

if 

f 

4£ 

4i| 

ti 

^. 

10 

9 

70 

88 

1 

4H 

f 

11 

8 

81 

li,9 

32 

4 

44 

41^. 

§i 

S 

12 

8 

65 

75 

Tb<- 

•fb- 

4 

it 

t 

f 

13 

7 

65 

88 

Vs 

| 

8|S 

4| 

i 

if 

14   7 

51 

88 

£1 

| 

4i 

§1 

I 

15 

6 

50 

63 

it 

1 

3;T2 

3f 

ii 

ft 

16 

6 

40 

63 

f 

3 

H 

fi 

17 

5 

34 

40 

"Ftf 

iV 

2|i 

2H 

^ 

18 

5 

30 

40 

3T2 

-fff 

21 

2H 

i 

4 

19 

4 

28 

88 

-L 

i 

O'i 

3 

^ 

_ti 

20 

4 

18.5 

21.5 

| 

i 

2± 

t 

/2 

21 

3 

23 

28.6 

.1 

iV 

2^ 

2U 

1^6 

-L 

22 

3 

17 

21.7 

,8 

A 

24 

8 

« 

The  width  of  the  flange  varies  directly  with  the  thickness 
of  the  web. 


TABLES   OF  DIMENSIONS. 


WEIGHTS  OF  VARIOUS  WEB  THICKNESSES. 


PENCOYD 


BEAMS. 


Chart  Number. 

to  to  1  Ci  or  J  Depth  in  inches. 

-•  MI*  |  Minimum  Web  Thick- 
ness. 

Minimum  Weight  per 
yard. 

APPROXIMATE  WEIGHT  IN  POUNDS  PER  YARD  FOR  EACH 
THICKNESS  OP  WEB  IN  INCHES. 

(Calculated  upon  the  basis  that  one  Cubic  Foot  of  Iron 
weighs  480  Ibs.) 

1 

A 

a. 

A 

* 

5 

8 

t 

i 

1 

2 

8 

4 

200.0 
145.0 

214.0 
192.0 

233.0 

145.0 

154.5 

173.0 

fl 

168.0 
120.0 

179.0 
155.5 

194.0 

125.5 

140.5 

5 
54 
6 

1 

if 
if 

H 

134.4 
108.3 
89.3 

137.7 
118.1 
105.8 

150.8 
131.2 

111.6 
99.2 

92.6 

7 
8 

9 
10 

11 
12 

10 
10 

4 

111.7 
90.4 

111.7 
106.0 

124.2 

136.7 

93.6 

99.8 





9 
9 

8 
8 

c-J-cd- 

*-|CK.|W 

90.7 
69.8 

81.4 
65.3 

93.5 

82.4 

99.1 

88.1 

110.4 

121.6 



71.2 

76.8 

S 

83.9 
75.3 

88.9 

98.9 

108.9 

65.3 

70.3 

13 

14 

7 

7 

6 

6 

1! 

65.8 
51.4 

52^5 

56.9 

61  .'2 

65.8 
65.6 

70.2 
70.0 

78.9 
78.7 

87.7 
87  5 

15 

16 

ii 

50.0 
40.0 

53.0 
51.0 

55.5 
55.0 

63.0 
63.0 

40.0 

44.0 

47.5 

17 

18 

5 
5 

t 

34.0 
30.0 

aiis 

34.0 

34.0 

37.0 
37.8 

40.0 
40.9 

19 

20 

4 
4 

4 

28.0 
18.5 

28  0 
21.5 

30.5 

33.0 

35.5 

38.0 

21 
22 

3 
3 

A 

23  0 
17.0 

28  0 

19^8 

24.8 
21.7 

26.7 

28.6 

Beams  of  any  weight  between  the  minimum  and  maximum 
per  yard,  given  in  the  table,  can  be  furnished. 


weight 


4  WKOUGHT  IRON  AND   STEEL. 

SIZES  OF  MINIMUM  AND  MAXIMUM  SECTIONS. 


PENOOYD 


Q 


B 


i,  CHANNELS. 


I 

I 

ja 

0)     . 

« 

•  | 

cs 

3 

i 

I 

1 

«j 

fe'S 

^T3 

^   OD 

E  - 

1 

1 

Chart  Nun 

Size  in  inc 

Minimum 
per  ya 

Maximum 
perya 

Minimum 
Thicknf 

Maximum 
ThickiK 

Minimum 
Width 

Maximum 
Width 

H 

Flange  Thi 

A 

B 

B 

C 

C 

D 

E 

30 

15 

139.0 

204.5 

A 

1 

4 

41 

1 

8 

31 

12 

88  5 

160.0 

if 

1 

2f£ 

3U 

1 

A 

32    12 

60.0 

101.5 

jj 

m 

i! 

i 

U 

34   10 

60.0 

106.0 

A 

| 

2Af 

3iV 

T6 

A 

35   10 

49.0 

86.5 

5      1     2^ 

24 

i 

2 

36 

9 

53.0 

92.0 

j^. 

a      i     2-V 

27? 

a 

_1| 

37 

9 

37.0 

61.0 

it 

i 

2fi-4- 

241 

Ii 

64 

38 
39 

8 
8 

43.0 
30.0 

80.5 
r>4.0 

A 
If 

.    | 

85 
2 

n 

.4.-1 

11 

H 

40 
41 

7 
7 

41.  0 
26.0 

73.0 
49.0 

S 

| 

1 

2A 

1 

i 

42 

6 

31.9 

54.4 

1 

fi 

2| 

2$ 

A 

A 

43 

6 

27.6 

50.1 

-L 

5 

2 

2? 

ii 

1 

44 

6 

22.7 

39.6 

Ji 

| 

If 

2:,V 

ft 

45 

5 

27.3     46.0 

^ 

| 

2 

2S 

it 

46 

5 

18.8     32.9 

A 

i 

15. 

Iff 

1 

tV 

47 

4 

21.5     31.5 

i 

-1- 

1H 

lit 

U 

i 

48 

4 

17.5     23.7 

A 

| 

i* 

T 

49 

3 

15.2      18.9 

A 

H 

1H 

Ifi 

H 

'i 

50 

§ 

11.3     11.3 

j 

4 

i 

H 

If 

i 

i 

51 

2 

8.75     10.0 

A 

3^ 

1A 

1A 

A 

A 

52 

If 

3.5 

3.5 

A 

A 

if 

U 

i 

A 

The  width  of  the  flange  varies  directly  with  the  thickness  oJ 
the  web. 


TABLES   OF  DIMENSIONS.  5 

WEIGHTS  OF  VARIOUS   WEB  THICKNESSES. 
FENCOYD     \ /CHANNELS. 


§  I  Chart  Number. 

c£  1  Depth  in  inches. 

-j  1  Minimum  Web 
Thickness. 

Minimum  Weight 
per  yard. 

APPROXIMATE  WEIGHT  IN  POUNDS  PER  YARD  FOR  EACH 
THICKNESS  OF  WEB  IN  INCHES. 

Calculated  upon  the  basis  that  one  Cubic  Foot  of  Iron 
weighs  480  Ibs. 

i 

& 

I 

& 

i 

5. 

I 

1 

1 

1 

139.0 

- 

148.0 

167.0 

186.0 

204.5 

31 

32 

34 
35 

12 

12 

10 
10 

if 
& 

~#~ 

88.5 
60.0 

92.0 
79.0 

100.0 
86.5 

115.0 
101.5 

130.0 

145.0 

160.0 

49!6 

64.0 

63.0 
55.0 

71.5 

60.0 
49.0 

69.0 
61.5 

75.5 

67.0 

81.0 
74.0 

94.0 
86.5 

106.0 



92^0 

30 

37 

9 
9 

8 
8 

7 
7 

fk 
if 

53  .  0 
37.0 

.... 

53.0 
44.0 

45.5 
39.0 

58.5164.0 
49.555.0 

70.0 
61.0 

81.0 

38 
31) 

40 
41 

A 
Jl 

43.0 
30.0 

3i!6 

50.5 
44.0 

55.5 
49.0 

51.0 
44  5 

60.5 
54.0 

55.0 
49.0 

70.5 

80.5 





64.0 

73.0 





ig 

s 

41.0 
26.0 

3i!s 

42.0 
36.0 

46.5 
40.0 

39.4 
35.1 
32.1 

33.5 
2G.6 

26.5 
23.7 

42 
43 
44 

45 
46 

47 

48 

49 
50 

I 

6 

5 
5 

4 
4 

3 
2i 

A 
I 

1 

A 

~& 
i 

31.9 
27.6 
22.7 

27.3 

18.8 

21.5 
17.5 

15.2 
11.3 

31.9 
27.6! 

±3 

27.3 

20.4 

21.5 
18.7 

16.1 
11.3 

35.6 
31.41 
28.3, 

30.4 
23.5 

24.0 
21.2 

18.0 

43.1 

38.9 
35.8 

3S.7 
29.7 

29.0 

46.9 
42.6 
39.6 

54.4 
50.1 



39.8 
32.9 

46.0 







31.5 



— 



51 
52 

2 
If 

A 

8.75 

9.4 









~  — 

A 

3.5 

Channels  of  any  weight  between 
weight  per  yard,  given  in  the  table, 


the  minimum  and  maximum 
can  be  furnished. 


6  WROUGHT  IRON  AND   STEEL. 

SIZES  OF  MINIMUM  AND  MAXIMUM  SECTIONS. 


PENCOYD 


B 


Pi?DECK  BEAMS. 


Chart  Number.  , 

Size  in  inches. 

'Ec 

ti 

11 

c 

s 

Maximum  Weight 
per  yard. 

Minimum  Web 
Thickness. 

Maximum  Web 
Thickness. 

Minimum  Flange 
Width. 

Maximum  Flange 
Width. 

Minimum  Bulb 
Width. 

Maximum  Bulb 
Width. 

Bulb  Depth. 

Flange  Thickness. 

Flange  Thickness.] 

A 

B 

B 

C 

C 

F 

F 

G 

D 

E 

(>(> 

12 

104.0 

138.0 

H 

tt 

51 

6& 

OJ. 

'•'B 

2^i 

If 

M 

if 

Gl 

11 

91.0 

118.0 

1 

| 

5i 

51 

2 

2i 

H 

a 

4 

ft 

62 

10 

80.0 

105.0 

3 

1 

&i 

&i 

ii 

2i 

HI 

H 

ii 

6;] 

9 

72.0 

94.0 

3. 

» 

B 

H 

5 

5i 

m 

2A- 

Hi 

1 

f 

04 

8 

61.0 

84.0 

ft 

1 

4£ 

4ff 

m 

m 

1A 

tt 

H 

65 

7 

52.0 

72.0 

H 

| 

41 

4M 

ii 

iii 

1A 

1% 

tV 

GO 

6 

42.0 

57.0 

A 

A 

81 

4 

1A 

1U 

1^ 

H 

A 

67 

5 

34.0 

46.0 

rv 

A 

H 

8| 

iA 

l-i2,; 

-it 

i 

I 

TABLES   OF  DIMENSIONS.  7 

WEIGHTS  OF  VARIOUS  WEB  THICKNESSES. 


PENCOYD 


o 


DECK  BEAMS. 


Depth  in  inches.  | 

Minimum  Web  Thick- 
ness. 

Minimum  Weight  per 
yard. 

APPROXIMATE  WEIGHT  IN  POUNDS  PER  YARD  FOR 
EACH  THICKNESS  OP  WEB  IN  INCHES. 

Calculated  upon  the  basis  that  one  Cubic  Foot  of  Iron 
weighs  480  Ibs. 

i 

A 

a 

8 

A 

i 

A 

1 

ti 

12 

i  i 
.j  -i 

a 

« 

104.0 

108.0 

115.0 

123.0 

130.0 

138.0 

11 

91.0 

91.0 

98.0 

105.0 

111.0 

118.0 



10 

a. 

80.0 

80.0 

86.0 

92.0 

99  0 

105.0 

9 

n 

8 

72.0 

.... 

.... 

72.0 

77.0 

83.0 

89.0 

94.0 

8 
7 

& 

61.0 

64  0 

69.0 

74.0 

79.0 

84.0 

H 

52.0 

54.0 

58.0 

63.0 

67.0 

72.0 

42.0 

6 
5 

A 

A 

42.0 

.... 

46.0 

49.0 

53.0 

57.0 

84.0 

.... 

34.0 

37.0 

40.0 

43.0 

46.0 

WROUGHT  IRON  AND   STEEL. 


PENCOYD 


ANGLES. 


EVEN  LEGS. 


WEIGHTS  PER  YARD  OF  VARIOUS  THICKNESSES. 
One  cubic  foot  weighing  480  Ibs. 


Chart 
Number. 

SIZE  IN 
INCHES. 

1" 

-.V 

i" 

iV' 

1" 

71.1 

U" 

t" 

ir 

I" 

1" 

120 

6    x6 

50.6 

57.5 

64.3 

77.8 

84.4 
69.4 

90.6 

97.3 

110.0 

121 

5   x5 

41.8 

47.5 
37.5 

53.1 

41.8 

58.6 
46.1 

(54.0 
50.3 

74.7 

79.8 

90.0 

122 

4   x4   28.6 

33.1 

54.4 

123 

3£x3£ 

24.8 
i" 

8 

28.7 

-a," 

32.5 

J." 
4 

36.2 

A-" 

3D.  8 
1" 

iV' 

T 

iV' 

5." 
« 

124 

3    x3 

14.4 

17.8 

21.1 

24.3 
22.1 

27.5 

30.6 

33.6 

125 

2Jx23 

13.1 

16.2 

19.2 

25.0 

126 

2j  x  2i 

11.9 

14.6 
13.1 

17.3 
15.5 

19.9 
17.8 

22.5 





127 

01  v  Ol 
w4  X  ~4 

10.6 

128 

2    x2 



7.1 

9.4 

11.513.6.... 





...  . 

129 

11*11 

6.2 

8.1 

9.9 

11.7 





130 

HxU 



5.3 
4.3 

6.9 

5.6 

8.4 

9.8 









131 

lixii 

3.0 



132 

1    xl 

2.3 

3.4 

4.4 

TABLE   OF  DIMENSIONS. 


PENCOYD 


ANGLES. 


UNEVEN  LEGS. 

WEIGHTS  PER  YARD  OF  VARIOUS  THICKNESSES. 
One  cubic  foot  weighing  480  Ibs. 


Chart 
Number. 

SIZE 

IN 

INCHES 

i 

A 

3. 

a 

* 

41.  £ 
37.4 
35.1 
33.0 

\ 

47.5 
42.5 
40.0 

^ 

53.0 
47.4 
44.6 

f 

1 

I 

79.8 
71.1 

1 

90.0 
80.0 

140 

6    x4 

.... 

58.6 
52.3 
49.2 
46.0 

69.4 
61.8 

141 

5   x4 

.... 

— 

32.3 
30.5 

142 

5    xS^ 

58.1 

143 

5    x3 

.... 

28.6 

37.5 

41.7 

54.4 

.... 

144 

4£x3 

.... 

.... 

26.730.935.0 

S9.0 

43.0 

.... 



145 

4    x3£ 

26.7 

CO  935.0 

S9.0J43.0 



146 

4   x3 

.... 

21.024.8^8.732.536.239.8 



_ 

147 

3^x3 

.... 

23.026.5 

30.033.4 

36.7 

148 

3   x2i 

11.9 

16.219.222.125.0 
14.617.319.9I22.5 



149   3  x2 

150   3£x2£ 

17.8 

21.1 
34.5 

24  3 

27.5 

85.0 

151 

6    x3£ 

... 

39.645.0! 

50.3 

55.5165.6 

| 

5.5 

152 
153 

6|x4 



~ 

32.3 

44.0 
37.4 

50.055.9 

61.7 

73.1 

84.295.0 

Si  x  3.} 

42.5 

47.4 

52.3 
61.7 

73.1 

84.2 

95.0 

154 

7    x3£ 

• 

155 

2^x2 

10.6 

13.1 

15.4 

17.7 

20.0 









156 

aixu 

8.7 

10.7 

12.6 



157 

2    xl-i 

7.5 

9.2 

10.8 

10 


WROUGHT  IRON  AND   STEEL. 


PENCOYD 


ANGLES. 


SQUARE   BOOT. 

WEIGHTS  PER  YARD  OF  VARIOUS  THICKNESSES. 
One  cubic  foot  weighing  480  Ibs. 


CHART 
NUMBER. 

160 

SIZE  IN 

INCHES. 

i 

A 

i 

ft 

• 

ft 

i 

A 

I 

4x4 

28.6 

33.0 

37.6 

41.8 

46.0 

161 

3^x3^ 

20.8 

24.8 

28.7 

32.5 

14'.  4 

162 

3x3 

17.8 

21.2 

>4.4 

27.5 

163 
164 

2fx2f 

2^x2i 

— 

— 

13.1 
11.9 

16.2 
14.6 

19.2 

i7! 

22.1 
19.9 

25.0 

.... 



.... 

165 
166 

3i  x  2* 

10.6 

13.1 
11.5 

15.5 

17.8 





2x2 

..... 

... 

9.4 

13.6 

.... 

.... 

167 

If-  a  If 

8.1 
6.9 

9.9 

8.4 

11.7 









168 

li  x  H 

.... 

5.3 

169 

U  x  H 

.... 

4.3 

5.6 

7.0 

.... 

.... 

.... 

....u... 

170 

1x1 

2.3 

3.4 

4.4 











171 

U  x  {f 

5  9 

TABLES   OF  DIMENSIONS. 

; —  — ^ 


11 


PENCOYD 


TEES. 


EVEN   LEGS. 


Chart  Number. 

Width  of  base. 

g 

5 

<s 

1 

w 

Thickness  of 
base. 

Thickness  of 
base. 

Thickness  of 
stem. 

Thickness  of 
stem. 

WEIGHT 
PER  YARD. 

A 

B 

D 

E 

C 

F 

70 

4 

4 

& 

ft 

^ 

i 

36.51bs. 

71 

9* 

8i 

ft 

i 

iV 

i 

31.01bs. 

72 

3 

3 

H 

if 

-i\ 

i 

SC.Olbs. 

73 

2i 

2i 

if 

if 

H 

if 

19.51bs. 

74 

2* 

2i 

H 

if 

tt 

if 

17.52  Ibs. 

75 

3* 

2i 

i 

3 

¥ 

i 

i 

11.751bs. 

76 

2i 

^ 

i 

1% 

i 

4 

A 

12.0  Ibs. 

77 

2 

2 

i 

4 

ft 

1 
4 

ft 

10.  5  Ibs. 

78 

if 

If 

ft 

i 

A 

i 

7.  libs. 

79 

H 

H 

A 

i 

A 

i 

6.0  Ibs. 

80 

n 

n 

ft 

i 

4 

tV 

i 

4.  5  Ibs. 

81 

i 

i 

A 

i 

A 

i 

3.0  Ibs. 

82 

3 

3 

TO 

1 

ft 

3. 

f 

19.  a  Ibs. 

83 

3 

3 

2 

ft 

3. 

« 

ft 

22.  6  Ibs. 

Weights  of  these  sections  cannot  be  varied. 


12 


WBOUGHT  IKON  AND   STEEL. 


PENCOYD 


TESS. 


UNEVEN  LEGS. 


Chart  Number. 

Width  of  base. 

Height  of  stem. 

Thickness  of 
base. 

Thickness  of 
base. 

Thickness  of 
stem. 

H 

c  g 

Is 

2 
H 

WEIGHT 
PER  YARD. 

A 

B 

D 

E 

C 

F 

90 

4i 

8* 

A 

i 

H 

i 

44.51bs. 

91 

4 

8J 

A 

t 

A 

u.  . 

4 

41.81bs. 

92 

5 

2i 

1 

| 

A 

g 

30.71bs. 

93 

5 

•ft 

A 

A 

A 

1* 

33.01bs. 

94 

4 

3 

a 

« 

A  . 

t 

£ 

25.91bs. 

95 

4 

3 

5 

A 

A 

| 

25.251bs. 

96 

4 

2 

4 

T^ 

t 

1^ 

20.41bs. 

97 

3 

8ft 

A 

i 

iV 

f 

28.25  Ibs. 

98 

3 

8i 

a. 

A 

i 

I 

23.81bs. 

99 

3 

H 

1 

i 

± 
4 

i 

11.  2  Ibs. 

ICO 

*$ 

u 

1 

i 

4 

i 

A 

9.1  Ibs. 

101 

2 

H 

.  -4 

3% 

i 

A 

8  .  75  Ibs. 

102 

2 

1 

i 

1 
4 

i 

:r* 

7.0  Ibs. 

103 

2 

A 

i 

4 

1 
4 

A 

5 

TiT 

5.88  Ibs. 

104 

2f 

if 

4 

H 

i 

3. 
4 

18.  75  Ibs. 

105 

2f 

2 

A 

ii 

n 

4 

t 

21.0  Ibs. 

106 

5 

3* 

i 

i 

i* 

| 

48.  4  Ibs. 

107 

5 

4 

i 

i 

i 

a 

44.1  Ibs. 

108 

2* 

iaff 

| 

i 

A 

^ 

6.  5  Ibs. 

109 

4 

g 

A 

,5. 

A 

i 

38.  5  Ibs. 

110 

3 

2* 

A 

4 

-5-r 

a 

17.  6  Ibs. 

111 

3 

SJft 

a. 

i 

A 

A 

t 

20.  6  Ibs. 

Weights  of  these  sections  cannot  be  varied. 


TABLES    OF  DIMENSIONS. 


13 


PENCOYD 


ANGLE  COVERS. 


WEIGHTS  PER  YARD  OF    VARIOUS   THICKNESSES. 


One  cubic  fo'ot  weighing  480  Ibs. 


CHAKT 
NUMBER. 

180 
181 

SIZE  IN 
INCHES. 

3x3 

2f  x  2J 

i 

1*6 

i 

14.3 
13.0 
11.8 
10.5 

A 

17.7 
16.1 
14.5 
13.0 

t 
21.0 
19.1 
17.2 
15.4 

f* 

24.2 

* 

27.4 
24.9 

<» 

ITS 

30.5 

I 
33.5 



22.0 



182 
183 

2|x2£ 
2i-  x  2| 

19.9 

17.7 

22.4 







.... 

184 

2x2 

.... 

7.0 

9.3 

11.4 

13.5 

.... 

.... 

.... 

.... 













— 


WROUGHT   IRON  AND   STEEL. 
SIZES  OF  PENCOYD  BAR  IRON. 


FLATS. 


1 

x 

if    inches  to   f    inches. 

2A- 

x 

\\  inches  to  2 

inches. 

1 

X 

i 

(               1            « 

2|b 

x 

*       "         It 

** 

I7/? 

X 

^ 

1 

2i 

x 

i       ••         2 

tt 

ITU" 

x 

I 

.             -^                « 

X 

i       "         2t 

<< 

It 

X 

I 

1 

afe 

x 

It       "         2t 

« 

IT\T 

X 

b. 

8 

1 

3 

x 

'      at 

« 

if 

x 

x 

|                i 

1               " 
1 

31 

x 

X 

1| 

3 
2 

ft 

if 

x 

X 

| 

1 

I 

3t 
4 

X 

X 

1 

2 
3t 

<( 

14> 

X 

«                        '1  -jJg- 

( 

44- 

x 

4" 

2 

ft 

IrV 

x 

tt                 "                iVfr 

* 

5 

x 

? 

3t 

« 

It 

x 

"1                     "                11 

( 

6 

X 

i 

'         3 

t 

l^f 

X 

"          I'll? 

' 

7 

X 

3 

< 

!«" 

X 

i         "       IfV 

< 

8 

X 

1 

<         2^ 

f 

If 

X 

JL              «           |i 

< 

9 

X 

i. 

<         21 

« 

lit 

X 

1               "           l| 

< 

10 

X 

JL 

'         21 

t 

2 

If 

X 
X 
X 

i     "    ll, 
i     «    it 

11 

12 

X 

X 

1 

'     l\ 

~ 

SQUARES. 

t",  -iV,  f",  H",  t",  it",  i",  if",  i",  w,  n",  w, 

H",  1|",  1|",  ir',  If",  U",  2",  24",  2t",  2|",  3",  3-1", 
3V,  3|",  4"  and  44". 

ROUNDS. 

M",  14",  i".  If",  iV,  ti",  I!",  IS",  f",  H",  tt", 
H",  H",  f",  Jl",  IS".  M",  €i",  M",  F',  H",  tt",  II". 
•Si",  II",  i",  W,  W,  life",  lt",'iA",  W,  1^", 

14",  itr,  i^",  U",  i-.v,  it",  w,  if,  if",  ij", 

2",  2F,  21",  2|",  2t",  at",  21",  21-",  3",  8t",  31",  8f",  3f'f  3f", 
8f",  3|",  4",  44",  41",  4f ",  44",  4f',  4|",  4J",  5",  51",  64",  5|", 
6",  6^"  and  7". 

HALF  ROUNDS. 


i",  1",  11",  It",  1|" ,  2",  21",  2^,  2f",  3",  34"  and  34". 


MISCELLANEOUS  SHAPES. 


15 


Two  grades  of  iron  are  manufactured,  known  respectively  as 
"  Pencoyd  Refined  "  and  "  Pencoyd  High  Test,"  the  former  for 
all  ordinary  requirements,  the  latter  for  tension  members  of 
structures  and  all  purposes  where  a  uniform  iron  of  high  duc- 
tility is  required. 

10  X  AREA  IN  INCHES  =  WEIGHT  PER  YARD  IN  LBS. 

In  any  rolled  section  of  wrought  iron,  the  weight  in  Ibs.  per 
yard,  is  precisely  equal  to  ten  times  its  sectional  area  in  square 
inches. 

Consequently,  either  value  being  known,  the  other  can  be  in- 
stantly obtained. 


AXLES. 


M^ 


U$ 


TT* 


U- 


'  // 
-W*- 


J 


MASTER  CAR  BUILDERS'  STANDARD-AXLE 

Hammered  or  rolled  axles  of  iron  or  steel,  centred  and 
straightened  with  journals  forged  or  rough-turned,  made  to  con- 
form to  specifications  and  tests. 


STRUCTURAL  WORK. 

The  fitting,  punching,  and  riveting  of  structural  work  exe- 
cuted, and  iron  castings  furnished  to  order. 


15  WROUGHT  IRON  AND   STEEL. 

MISCELLANEOUS  SHAPES. 


CAR  BUILDERS'  CHANNEL. 

Chart  No.  33. 
Weight  per  yard  =  50  to  55  Ibs. 


TEN-INCH  BULB  PLATE. 

Chart  No.  68. 
Weight  per  yard  =  62  Ibs. 


MINERS'  TRACK  RAIL. 

Chart  No.  190. 
Weight  per  yard  =  25  Ibs. 


SPLICE  BAR  FOR  MINERS'  TRACK  RAIL. 

Chart  No.  191. 
Weight  per  yard  =  5.2  Ibs. 


SLOT  RAIL  FOR  CABLE  ROAD. 

Chart  No.  192. 
Weight  per  yard  =  26  Ibs. 


HALF  OVALS. 

Chart  No.  193  =  4.3  Ibs.  per  yd. 
Chart  No.  194  =  4.8  Ibs.  per  yd. 

Channel  Rail.     Chart  No.  195  =  3.5  Ibs.  per  yard. 


GROOVED  BARS. 

Chart  No.  196  =    8.4  to  14.7  Ibs.  per  yard. 

197  =  1 3  5  to  21 . 0  Ibs.  per  yard. 

"         198  =  20 . 9  to  34  5  Ibs.  per  yard. 


STRENGTH  OF  WROUGHT  IRON. 
STRENGTH  OF  WROUGHT  IRON. 


17 


The  tensile  strength  of  rolled  iron  varies  according  to  the  quality 
of  the  material,  the  mode  of  manufacture,  and  the  sectional  area 
of  the  bar.  In  general  terms  the  ordinary  sizes  of  bars  of  good 
material  may  be  accepted  as  having  an  ultimate  tensile  strength 
of  50,000  Ibs.  per  square  inch  of  section,  an  elastic  limit  of 
30,000  Ibs.,  and  will  stretch  20  per  cent,  in  a  length  of  8  inches 
when  tested  up  to  rupture. 

It  is,  however,  as  easy  to  produce  the  smaller  sizes  yielding 
results  10  per  cent,  higher  than  the  above,  as  it  is  difficult  to 
make  the  largest  sections  with  a  limit  10  per  cent,  below  the 
same  figures. 

Dividing  rolled  iron  into  three  classes  according  to  its  sectional 
area,  we  have: 

I. — Bars  not  exceeding  1$  square  inches  area. 
II. — Bars  from  H  to  4  square  inches  area. 

III. — Bars  from  4  to  8  square  inches  area. 

For  which  experiments  give  the  following  figures  as  average 
results. 


TENSILE    STRENGTH 

ELASTIC    LIMIT 

ELONGATION  IN 

CLASS. 

PER  SQ.  INCH. 

PEU  SQ.  INCH. 

8  INCHES. 

I. 

53,000  Ibs. 

33,000  Ibs. 

25  per  cent. 

II. 

50,000   " 

30,000   " 

20    "      «« 

III. 

48,000   " 

28,000   " 

18    "      " 

These,  however,  are  only  general  conclusions,  as  much  depends 
on  the  shape  of  the  section,  the  method  of  rolling,  and  the 
reduction  of  area  from  the  pile  to  the  finished  bar. 

The  following  tensile  tests  are  actual  averages  taken  from  our 
records,  and  were  made  on  specimens  cut  from  bars  of  the  sizes 
and  shapes  given,  and  intended  for  use  in  bridges,  and  to  con- 
form to  the  specifications  of  the  leading  railroad  companies. 
2 


18 


WROUGHT  IRON  AND   STEEL. 


SIZE  AND  SHAPE  OF 
BAR. 

Ultimate  strength 
in  Ibs.  Per  Square 
Inch. 

S| 

ik 
iifl 

«S  OB 

s^ 

Per  Cent,  of 
Elongation  in  8 
inches. 

Per  Cent,  of 
Reduction  of 
Fractured  Area. 

One-inch  rounds. 
Two-inch  rounds. 
Four-inch  rounds. 
Four-inch  flats. 
Eight-inch  flats. 
Twelve-inch  flats. 
Three-inch  angles. 
Six-inch  angles. 
Flanges  of  beams 
Webs  of  beams. 

52,210 
50,935 

48,220 
51,000 
49,500 
49,(J80 
49,000 
49,160 
51,840 
50,130, 

32,150 
31,800 
26,640 
30,000 
31,500 
31,560 
30,500 
30,150 
31,560 
30,150 

26 
19.8 
18 
20.7 
16 
15.5 
17 
18.1 
20.1 
17.7 

39 

31 
'30* 

f  to  H  in-  thick. 
%  inches  thick. 
|  inches  thick. 

COMPRESSION. 

The  power  of  wrought  iron  to  resist  compression  is  usually 
taken  as  equal  to  its  tensile  strength.  In  the  form  of  flanges  for 
solid  beams,  this  property  is  exerted  to  its  full  capacity,  as  the 
adjacent  portion  of  the  material  in  tension  sustains  the  portions 
in  compression  from  buckling,  even  when  the  length  of  the 
beam  becomes  very  considerable.  But  in  the  form  of  struts  and 
columns,  when  the  piece  becomes  of  considerable  length  in  pro- 
portion to  its  cross-section,  failure  occurs  by  bending,  or  com- 
bined bending  and  crushing.  (See  article  on  Struts.)  Judging 
from  many  experiments  we  have  made  on  bars  secured  from 
bending  under  compressive  stress,  the  elastic  limit  in  compres- 
sion is  a  little  lower  than  in  tension,  but  the  former  not  so  clearly 
defined  as  the  latter  ;  practically  they  may  be  considered  as 
equal. 

These  results  were  derived  from  small  sections;  in  large  sections 
there  may  be  more  equality,  as  some  experiments  hereafter  de- 
scribed would  denote. 

With  pressures  varying  from  25,000  to  35,000  Ibs.  per  square 
inch,  the  elastic  limit  is  attained.  With  50,000  Ibs.  per  square 
inch  a  permanent  reduction  of  2^  per  cent,  of  the  length  is  pro- 
duced; with  75,000  Ibs.  a  reduction  of  6  per  cent,  and  with 


ELASTICITY  OF  ROLLED  IRON.  19 

100,000  Ibs.  per  square  inch  the  permanent  reduction  of  length 
is  about  8  per  cent.  These  results  have  a  wide  range  of  varia- 
tion, bufe  the  figures  are  the  averages  of  several  experiments. 

ELASTICITY  OF  ROLLED  IRON. 

The  elasticity  of  wrought  iron,  or  its  ratio  of  change  of  length 
under  stress  below  the  elastic  limit,  varies  more  extensively  than 
any  other  property  of  rolled  iron.  Experiment  shows  a  varia- 
tion of  over  100  per  cent,  in  extreme  cases. 

The  modulus  of  elasticity  is  an  imaginary  load,  which,  suppos- 
ing the  material  to  be  perfectly  elastic,  would  cause  the  iron  to 
double  its  length  under  tension,  or  to  shorten  its  length  one-half 
under  compression,  and  return  to  its  original  length  when  re- 
leased from  stress.  This  modulus  is  usually  assumed  at  29,- 
000,000  Ibs.  In  large  sections  of  properly  prepared  material  the 
tensile  elasticity  probably  averages  a  little  over  this,  and  the 
compressive  elasticity  a  little  below  it. 

The  following  results  of  the  tests  for  comparative  elasticity  in 
tension  and  compression,  will  serve  to  illustrate  the  irregularity 
of  the  elasticity ;  also,  see  tests  of  iron  and  steel  cut  from  beams, 
given  hereafter. 


20 


WROUGHT  IRON  AND   STEEL. 


Two  pieces  of  3-inch  square  iron  cut  from  same  bar. 
Measured  length  of  each  specimen  =  12  inches. 
Area  of  each  specimen  =  .556  square  inch. 
Pressures  in  Ibs.  ;  change  of  length  in  inches. 


TENSILE  TEST. 

COMPRESSIVE  TEST. 

Elongations. 

Bednction  of  length. 

Pressure  per 
sq.  inch. 

Load  on. 

Load  off. 

Pressure  per 
sq.  inch. 

Load  on. 

Load  off. 

5,000 

.002 

.000 

5,000 

.002 

.000 

10,000 

.0045 

.000 

10,000 

.0035 

.000 

15,000 

.0065 

.000 

15,000 

.005 

.000 

20,000 

.0085 

.000 

20,000 

.006 

.000 

22,000 

.010 

.000 

22,000 

.007 

.000 

24,000 

.0105 

.000 

24,000 

.008 

.000 

26,000 

.0115 

.000 

26,000 

.009 

.000 

28,000 

.012 

.000 

28,000 

.0095 

.000 

30,000 

.013 

.000 

30,000 

.010 

.000 

32,000 

.0135 

.000 

32,000 

.011 

.000 

34,000 

.0145 

.000 

34,000 

.020 

.0035 

36,000 

.0155 

.001 

36,000 

.023 

.0045 

38,000 

.1715 

.1495 

38,000 

.027 

.010 

40,000 

.3835 

.3605 

40,000 

.107 

.089 

50,000 

1.326 

1.2945 

50,000 

.272 

.246 

53,820 

3.093 

60,000 

.464 

.435 

70,000 

.'671 

]639 

Specimen  broke  with  53,820 

80,000 

.845 

814 

Ibs.  per  square  inch. 

90,000 

1.074 

1.042 

Stretched  3.093  in  12  in. 

2.  187  in  8  in. 

Modulus  of  elasticity 

"      27.  3  per  cent,  in  8  in. 

=  35,300,000  Ibs. 

Fractured  area  =  .3364 

Modulus  of  elasticity 

=  27,420,000  Ibs. 


ELASTICITY  OF  EOLLED   IRON. 


21 


Two  pieces  of  ^-inch  round  iron  cut  from  same  bar. 
Measured  length  of  each  specimen  =  12  inches. 
Area  of  each  specimen  =  .449  square  inch. 
Pressure  in  Ibs. ;  change  of  length  in  inches. 


TENSILE  TEST. 

COMPRESSION  TEST. 

Elongations. 

Reduction  of  length. 

Pressure  per 

Load  on. 

Load  off. 

Pressure  per 

Load  on. 

Load  off. 

sq.  inch. 

sq.  inch. 

5,000 

.002 

.000 

5,000 

.002 

.000 

10,000 

.004 

.000 

10,000 

.005 

.000 

15,000 

.OC6 

.000 

15,000. 

.007 

.000 

20,000 

.008 

.000 

20,000 

.010 

.000 

2,1,000 

.009 

.000 

2-J.OOO 

.011 

.001 

24,003 

.010 

.000 

24,000 

.012 

.002 

26,000 

.0105 

.000 

26,000 

.013 

.003 

28,000 

.011 

.000 

28,000 

.015 

.0045 

30,000 

.013 

.000 

30,000 

.o-as 

.0065 

32,000 

.014 

.('00 

32,000 

.02-^5 

.007 

34,000 

.015 

.002 

34.000 

.0275 

.009 

30,000 

.022 

.007 

36,000 

.040 

.019 

38,000 

.416 

.399 

38,000 

.052 

.036 

40,000 

.544 

.52  3 

40,000 

.133 

.114 

50,000 

1.740 

1.707 

50,000 

.304 

.283 

51,600 

2.468 



60,000 

.427 

.402 

70,000 

.546 

.521 

Specimen  broke  with  51,600 

80,000 

.663 

.635 

Ibs.  per  square  inch. 

90,000 

.773 

.742 

Stretched  2.  468  in  12  in. 

100,000 

.896 

.862 

1.81  in  8  in. 

"      22.  6  per  cent,  in  8  in. 

Modulus  of  elasticity 

Fractured  area  =  .297  sq.  in. 

Modulus  of  elasticity 

=  29,400,000  Ibs. 


=24,490,000  Ibs. 


22 


WROUGHT  IRON  AND  STEEL. 


A  series  of  tests  was  made  on  the  United  States  Government 
testing  machine  at  Watertown  Arsenal,  on  the  full-sized  bars, 
of  which  the  following  is  a  condensed  average. 

TENSILE    TESTS. 


Kd" 

c   . 

gh 

£ 

a 

|* 

""  o 

«ft 

MODE  OF  MANU- 

JS 

Zo, 

-^  — 

*  gf 

tSjf 

o 
c 

VjD 

o 

•85  . 

ll 

FACTURE. 

g""1 

•~  ^ 

"  —  C 

a 

•p 

'-  S.S 

«5 

^<S  8 

"o 

1 

B" 

s 

£ 

* 

Single  rolled.  . 

3x1 

50,000 

28,600 

29 

28,200,000 

Double  rolled.  . 

3x1 

52,503 

30,100 

32 

27,885,000 

Single  rolled  .  . 

5xli 

49,800 

26,  100 

21 

27,930,000 

Double  rolled.  . 

5x11 

51,000 

27,200 

28 

28,920,000 

The  "single  and  double  rolled  "  means  the  number  of  work- 
ings from  the  puddled  bar. 

A  number  of  experiments  on  large  columns  with  the  same 
machine  gave  the  following  results, — also  the  tensile  results, 
for  the  iron  used  in  the  construction  of  the  columns. 


ELASTIC  LIMIT. 

MODULUS  OF 
ELASTICITY. 

Wrought  iron  in  compression  
Wrought  iron  in  tension     

27,500 
31,  GOO 

29,  COO,  000 
£9,100,000 

The  modulus  of  transverse  elasticity  as  applied  to  our  tables  of 
deflections  is  taken  at  26,000,000  Ibs.  It  is  a  hypothetical  quan- 
tity, derived  by  means  of  formulae,  which  are  given  elsewhere, 
and  which  assume  that  the  resistances  to  tension  and  compression 
are  equal,  and  that  the  successive  fibres  of  iron,  from  the  neu- 


SHEARING   AND  TORSION.  23 

tral  axis  outward  act  independently  of  each  other,  neither  of 
which  statements  are  correct  in  fact. 

It  is  probable  that  this  modulus,  with  the  same  material,  will 
vary  with  each  change  of  section,  and  possibly  also  with  changes 
of  length,  and  conditions  of  load. 

SHEARING. 

Under  the  conditions  that  shearing  stresses  are  usually  applied 
in  structures,  the  shearing  strength  of  wrought  iron  is  about 
eight-tenths  of  the  tensile,  viz.,  40,000  Ibs.  per  square  inch  of 
section.  But  when  subjected  to  the  action  of  properly  prepared 
cutting  knives,  the  resistance  to  shearing  is  much  less  than  this. 

TORSION. 

The  resistance  to  twisting  is  proportional  to  the  cube  of  the 
diameter.  When  the  shearing  strength  is  known,  the  torsional 
strength  of  any  round  shaft  can  be  determined  as  follows  :  T  = 
1.57  sr3.  r  —  radius  of  shaft  in  inches,  s  —  shearing  strength 
in  Ibs.  per  square  inch.  T  =  the  torsional  moment  in  inch  Ibs., 
or  the  force  in  Ibs.  multiplied  by  the  leverage  in  inches  with 
which  it  acts. 

In  practice,  however,  torsion  is  usually  accompanied  by  bend- 
ing stresses,  which  must  be  always  considered  when  determining 
the  proportions  of  shafts.  See  article  on  Shafting,  page  170. 


WROUGHT   IRON  AND   STEEL. 


STRUCTURAL  STEEL. 

The  various  grades  of  steel  used  in  structures  possess  such  an 
extended  range  of  physical  properties  that  it  is  impossible  to 
present  as  definite  a  basis  for  strength,  stiffness,  etc.,  as  can  be 
given  for  wrought  iron. 

The  character  of  the  material  is  largely  determined  by  its 
combination,  in  minute  proportions,  with  various  substances,  the 
most  important  of  which  is  carbon. 

As  a  general  rule  the  greater  the  percentage  of  carbon  in  the 
steel,  the  higher  will  be  its  tensile  strength  and  the  lower  its 
ductility.  The  following  list  exhibits  the  average  tensile  re- 
sistances for  steels  having  given  proportions  of  carbon : 


PERCENTAGE 
or  CARBON. 

TENSILE  STRENGTH  IN  POUNDS  PER 
SQUARE  INCH. 

DUCTILITY. 

ULTIMATE 
TENACITY. 

ELASTIC  LIMIT. 

ULTIMATE  ELONGA- 
TION IN  8  INCHES. 

.10 

60000 

36000 

26  per  cent. 

.15 

G6000 

40000 

24 

.20 

74000 

45000 

22 

.25 

82000 

50000 

20 

.30 

90000 

55000 

18 

.35 

100000 

60000 

16 

.40 

110000 

65000 

14 

These  figures,  however,  are  only  approximate,  as  much  de- 
pends on  the  quality  of  the  steel,  and  also  the  extent  to  which 
it  has  been  worked  in  the  rolling  process. 

The  grades  below  .15  per  cent,  carbon  are  known  conven- 
tionally as  "  mild  steels,"  owing  to  their  high  ductility  and  to 
their  possessing  but  very  moderate  hardening  properties  when 
chilled  in  water  from  a  red  heat. 


STRUCTURAL  STEEL.  25 

The  mild  steel  has  also  superior  welding  properties,  as  com- 
pared with  hard  steel,  and  will  endure  higher  heat  without 
injury. 

Steel  whose  carbon  ratio  does  not  exceed  .  10  per  cent,  should 
be  capable  of  doubling  flat  without  fracture,  when  chilled  in  the 
coldest  water  from  a  red  heat. 

Steel  of  .12  carbon  should  endure  similar  treatment  when 
chilled  in  water  of  80°  F. 

When  the  carbon  percentage  is  .  15  the  steel  should  be  capable 
of  bending  at  least  90°,  over  a  curve  whose  radius  is  three  or 
four  times  the  thickness  of  the  specimen  operated  upon,  and 
after  being  chilled  from  a  red  heat  in  water  of  80°  F. 

Steel  having  .35  to  .40  per  cent,  carbon,  will  usually  harden 
sufficiently  to  cut  soft  iron,  and  maintain  an  edge. 

There  is  much  variation  from  the  aforesaid  hardening  proper- 
ties in  different  qualities  of  steel,  as  much  depends  on  the  influ- 
ence of  other  hardening  agents  besides  carbon. 

The  modern  tendency  is  to  limit  the  use  of  steel  for  structural 
purposes  to  the  milder  grades  of  the  material.  For  steel  in 
steamships  the  United  States  Government  specifies  as  follows  : 
"  Steel  to  have  an  ultimate  tensile  strength  of  not  less  than 
60,000  Ibs.  per  square  inch,  and  a  ductility  of  not  less  than  25 
per  cent,  in  8  inches.  The  test  piece  to  be  heated  to  a  cherry- 
red  and  chilled  in  water  at  a  temperature  of  82°  F.  After  this 
it  must  be  capable  of  bending  double  flat  under  the  hammer 
without  cracking."  It  requires  about  .11  to  .12  carbon  steel  to 
endure  this  test. 

( '  Lloyd's  "  rules  require  the  steel  to  have  an^ultimate  tenacity 
of  not  less  than  60,000,  or  not  over  70,000  Ibs.  per  square  inch, 
with  an  elongation  of  at  least  16  per  cent,  in  8  inches.  This 
steel,  when  heated  to  redness  and  chilled  in  water  of  82°  F., 
must  bend  double  without  fracture  around  a  curve  of  which  the 
diameter  is  not  more  than  three  times  the  thickness  of  the  piece 
tested.  For  a  cold  test  without  hardening,  the  material  must  be 
capable  of  doubling  flat  and  bending  backward  without  fracture. 

Angles  and  beams  for  ship-frames  may  have  a  tenacity  of 
74,000  Ibs.,  providing  the  bending  tests  are  satisfactory,  and  the 
welding  property  is  unimpaired.  It  requires  about  .12  to  .14 
carbon  steel  to  meet  these  specifications. 


WROUGHT  IRON  AND  STEEL. 


We  have  made  numerous  experiments  on  steel  of  several 
grades  and  in  various  forms,  but  the  resistance  under  stress  is 
so  uncertain  that  a  fair  statement  of  its  physical  properties  can- 
not be  satisfactorily  given  until  an  exhaustive  series  of  experi- 
ments has  been  made  on  material  of  definite  composition. 

We  present  the  average  results  of  experiments  on  the  strength 
and  elasticity  of  "  mild  "  and  "  hard"  steel,  also  the  compara- 
tive resistance  of  these  materials  in  the  form  of  struts.  The 
"  mild  steel "  had  an  average  carbon  ratio  of  .12  per  cent.,  and 
the  "  hard  steel "  an  average  carbon  ratio  of  .36  per  cent.  The 
average  strength  and  elasticity  of  wrought  iron  is  inserted  for 
the  purpose  of  exhibiting  the  characteristics  of  the  steel  and 
iron.  As  in  the  case  of  the  steel,  the  several  values  given  for 
iron  are  the  results  of  a  few  special  experiments. 


MATERIAL. 

TENSILE  STRENGTH  IN 
LBS.  PER  SQUARE  INCH. 

DUCTILITY. 

MODULUS  op 
ELASTICITY  IN 
LBS. 

ULTIMATE 
TENACITY. 

ELASTIC 
LIMIT. 

ELONGATION  IN 
8  INCHES. 

Iron  

51000 
64000 
100000 

31000 
39000 
56700 

19  per  cent. 
24 
18 

28400000 
29300000 
29280000 

Mild  steel.... 
Hard  steel  

From  the  same  material  the  following  results  for  compression 
were  obtained. 

COMPRESSIVE  RESISTANCE. 


MATERIAL. 

ELASTIC  LIMIT  IN  LBS. 
PBR  SQUARE  INCH. 

MODULUS  OF 
ELASTICITY. 

Iron  

29500 

27090000 

Mild  steel 

37400 

24760000 

Hard  steel  

55700 

24570000 

STRUCTURAL   STEEL. 


27 


TRANSVERSE  STRENGTH. 

A  series  of  experiments  was  made  on  the  transverse  strength 
and  elasticity  of  round  bars  from  3  to  4  inches  in  diameter,  and 
flanged  beams  varying  from  3  to  12  inches  deep,  and  from  3  feet 
to  20  feet  in  length.  For  the  purpose  of  making  a  compact  ex- 
hibit of  the  resistance  of  beams  of  various  lengths  and  cross  sec- 
tions, the  results  of  the  experiments  were  condensed  to  the 
method  of  the  ensuing  table,  in  which 

R  =  the  modulus  of  maximum  resistance. 

JRV  =  the  modulus  of  resistance  at  the  elastic  limit. 

E  —  the  modulus  of  transverse  elasticity. 

_,       -.        bending  moment  x  depth  of  beam 

H  or  H\.  — n i 7^ * 

2  x  inertia 


_  Weight  x  cube  of  length  t 
~~  48  x  Inertia  x  deflection 

The  ultimate  resistance  was  taken  at  that  stage  of  the  experi- 
ment where  increase  of  deflection  occurred  without  increase  of 
load. 


MATERIAL. 

R 

By. 

E 

Iron 

44700  Ibs 

31000  Ibs 

27600000  Ibs. 

Mild  steel  

52800  " 

39500  " 

2970000D  " 

Hard  steel  

80200  " 

54500  " 

27200000  " 

As  is  well  known,  the  elasticity  of  iron  is  so  variable  and 
uncertain,  that  no  definite  value  can  be  assigned  to  it  except 
by  taking  the  averages  of  numerous  experiments.  Steel 
possesses  the  same  uncertain  elasticity,  especially  under  trans- 
verse and  compressive  stresses. 

The  elastic  moduli  in  tension  varied  from  27  to  33  millions  of 


28 


WROUGHT   IRON  AND   STEEL. 


pounds,  in  compression  from  21  to  33  millions,  and  transversely 
the  modulus  oJt'  elasticity  varied  from  23  to  33  millions  of 
pounds. 

It  is  probable  that  there  is  not  much  difference  on  the  whole 
between  the  transverse  elasticity  of  iron  and  either  grade  of 
steel;  if  any  difference  at  all  exists,  the  steel  probably  has  the 
advantage  in  stiffness,  and  the  experiments  indicate  that  the 
mild  steel,  if  anything,  is  stiffer  than  the  hard  steel,  the  reverse 
of  what  is  popularly  supposed  to  be  the  case. 

STEEL  BEAMS. 

The  experiments  demonstrate  that  the  transverse  resistance  of 
steel  of  different  grades  maintains  a  ratio  practically  uniform 
with  the  tenacities  of  the  different  steels.  Consequently  when 
steel  of  known  tensile  strength  is  used  in  beams,  the  absolute 
strength  of  the  beam  may  be  obtained  from  our  rules  and  tables 
for  iron  by  increasing  the  results  in  the  proportion  of  the  in- 
creased tenacity  of  the  particular  steel  used  over  that  of  iron. 
The  percentage  of  increase  for  good  qualities  of  steel,  will  be 
about  as  follows  : 


CARBON  PERCENTAGE. 

INCREASED  STRENGTH  OF  STEEL  OVER  WROUGHT 
IRON  BEAMS. 

.10 

20  per  cent  . 

.15 

35       " 

.20 

50      " 

.25 

65      " 

.30 

80      " 

The  experiments  do  not  show  that  steel  of  any  grade  is  stiffer 
under  working  loads  than  wrought  iron.  Therefore  beams  of 
either  steel  or  wrought  iron  having  uniform  lengths  and  cross 
sections  will  deflect  uniformly  under  equal  loads,  below  the  elas- 
tic limit  of  wrought  iron,  and  our  tables  of  deflections  for  iron 
beams  as  given  hereafter,  will  apply  also  to  steel. 


STRUCTURAL   STEEL.  29 

STEEL  SHAFTING. 

When  absolute  strength  irrespective  of  stiffness  is  alone  con- 
sidered, steel  probably  possesses  a  torsional  strength  exceeding 
that  of  iron  about  in  the  ratio  of  the  respective  tenacities  of  the 
two  metals.  Therefore,  when  designing  shafting  under  such 
conditions,  our  formulas  for  iron  shafting  can  be  used,  substitut- 
ing a  shearing  resistance  equal  to  f  of  the  tensile  strength 
of  the  steel,  in  place  of  that  given  for  iron  in  the  article  on 
Shafting.  But  in  the  large  majority  of  cases  the  usefulness  of 
shafting  is  determined  by  its  transverse  stiffness,  irrespective  of 
its  ultimate  torsional  strength. 

As  in  this  respect  the  advantage  of  steel  over  iron  is  very 
questionable,  it  will  be  found  necessary  to  use  the  same  dimen- 
sions of  steel  shafts  as  determined  by  our  rules  foi  wrought  iron. 

STEEL  STRUTS. 

The  experiments  on  direct  compression  prove  that  the  elastic 
limits  of  steel,  as  of  iron,  under  stresses  of  tension  and  com- 
pression, are  about  equal. 

Consequently  for  the  shortest  struts,  where  failure  results  from 
the  effects  of  direct  compression,  the  tensile  resistances  of  steel 
and  iron  serve  as  a  comparative  measure  of  the  strut  resistance 
of  the  two  materials. 

But  as  the  strut  is  increased  in  length,  and  failure  results 
from  lateral  flexure  before  the  compressive  limit  of  elasticity  is 
attained,  then  the  transverse  elasticity  of  the  material  becomes 
a  factor  of  increasing  importance  in  determining  the  strut  resist- 
ance. 

As  in  this  respect  the  steel  possesses  little  advantage,  if  any, 
over  iron,  the  tendency  will  be  for  struts  of  steel  and  iron  as  the 
length  is  increased  to  approximate  toward  equality  of  resist- 
ance. This  equality  with  iron  will  be  attained,  first  by  the 
mildest  steel,  and  latest  by  the  hardest  steel. 

The  results  of  many  experiments  we  have  made  seem  to  dem- 
onstrate that  this  equality  of  strut  resistance  is  practically 
attained  between  iron  and  mild  steel,  when  the  ratio  of  length 
to  least  radius  of  gyration  of  cross  section  is  about  200  to  1.  In 


30  WROUGHT  IRON  AND  STEEL. 

the  case  of  the  harder  steels,  practical  equality  of  resistance 
would  probably  be  reached  at  some  higher  but  unknown  ratio  of 
length  to  section. 

We  give  a  table  exhibiting  the  comparative  resistances  per 
square  inch  of  section  for  flat-ended  struts  of  iron,  mild  steel, 
and  hard  steel,  and  for  further  particulars  of  the  subject  refer 
to  the  article  on  Struts,  given  hereafter. 

It  is  quite  probable  that  grades  of  steel  intermediate  between 
those  denoted  in  the  table  will  offer  intermediate  resistance  as 
struts,  in  the  ratio  of  their  percentage  of  carbon,  other  elements 
remaining  the  same. 

SPECIFIC  GRAVITY. 

The  specific  gravity  of  steel  and  iron  varies  according  to  the 
purity  of  the  metal,  and  also  to  the  degree  of  condensation  im- 
parted by  the  rolling  process. 

As  a  rule  the  mild  steel  has  a  higher  specific  gravity  than 
hard  steel,  and  both  are  denser  than  iron.  A  number  of  tests 
we  have  made  for  specific  gravity  show  rolled  bars  of  mild  steel 
to  vary  from  7.84  to  7.83,  and  hard  steel  from  7.81  to  7.85 
specific  gravity.  Ordinary  iron  bars  will  vary  from  7 . 6  to  7 . 8. 

In  the  form  of  beams  and  large  rolled  sections  generally,  the 
following  figures  may  be  accepted  as  a  fair  average. 

Material.  Weight,  per  cubic  foot.  Weight  per  cubic  inch. 

Mild  Steel 489.0  Ibs.  .283    Ib. 

Hard  Steel 486. G  "  .2815   " 

Iron 478.3  "  .2768   " 

Or  for  the  same  sectional  areas,  the  excess  in  weight  over  iron 
will  be,  for  mild  steel  2.24  per  cent,  and  for  hard  steel  1.7  per 
per  cent. 


STBUCTUEAL  S1 


FLAT-ENDED  ST 


ULTIMATE  RESISTANCE  IX  POUNDS   PEK   SQUARE  INCH    OF 
SECTION. 


UNIVERSITY 


LENGTH  DIVIDED 
BY  LEAST  RADIUS 
OF  GYRATION. 

IRON. 

MILD  STEEL. 
.12  CARBON. 

HARD  STEEL. 
.36  CARBON. 

20 

46000 

70000 

100000 

30 

43000 

51000 

74000 

40 

40000 

46000 

62000 

50 

38000 

44000 

60000 

60 

36000 

42000 

58000 

70 

31000 

40000 

55500 

80 

32000 

38000 

53000 

90 

30900 

36000 

49700 

100 

'29800 

34000 

46500 

110 

28000 

3200J 

43200 

120 

26300 

30000 

40000 

180 

24900 

2doco 

36700 

140 

23500 

26000 

33500 

150 

21750 

24000 

30700 

160 

20000 

220DO 

28000 

170 

18400 

20000 

25500 

180 

16800 

18000 

23000 

190 

15850 

1U300 

2101)0 

200 

14500 

14800 

19000 

210 

13600 

13600 

17200 

220 

12700 

12700 

15500 

230 

11950 

11950 

14400 

240 

11200 

11200 

13400 

250 

10500 

10500 

12400 

260 

98  0 

9800 

11500 

270 

9150 

9150 

10600 

280 

8500 

8500 

9700 

290 

7850 

7850 

9000 

300 

7200 

7200 

8500 

32  WROUGHT   IRON  AND   STEEL. 

RESISTANCE   TO  BENDING. 

When  wrought-iron  beams  are  subjected  to  bending  stresses, 
the  resulting  deflections  increase  nearly  in  direct  proportion  to 
the  increase  of  load,  up  to  the  limit  of  elasticity  of  the  iron. 
Slight  permanent  sets  can  be  observed  in  the  beam  before  the 
elastic  limit  is  reached,  just  as  similar  sets  are  obtained  in  longi- 
tudinal tests.  After  the  elastic  limit  is  passed,  the  deflections 
increase  in  a  greater  ratio  than  the  loads,  and  clearly  defined 
permanent  sets  occur,  until  another  stage  in  the  experiment  is 
reached,  when  the  beam  shows  increasing  deflection  without  any 
increase  of  load.  At  this  point  the  element  of  time  becomes  an 
important  factor.  The  load  can  be  very  slowly  increased,  with- 
out the  record  of  stress  showing  increase,  but  if  the  load  is  freely 
applied,  the  recorded  stress  may  be  very  considerably  augmented. 
It  is  probable  that  if  the  load  was  left  long  enough  on  the  beam 
at  this  stage  of  the  experiment  entire  failure  would  ensue. 

We  call  this  point,  which  can  generally  be  very  clearly  ob- 
served, the  "ultimate  resistance  "  of  the  beams,  and  whenever 
such  terms  as  "ultimate  load,"  "  breaking  load,"  etc.,  are  used 
in  connection  with  bending  stresses,  this  is  the  load  referred  to. 
The  stress  at  the  elastic  limit  bears  no  such  fixed  relation  to  the 
ultimate  stress  as  can  generally  be  observed  in  tensile  tests. 
The  length  of  the  beam,  and  probably  other  conditions,  such  as 
position  of  load,  etc.,  become  factors  in  determining  the  ratio, 
which  in  the  absence  of  complete  experiments  cannot  be  decided. 


MODULUS  OF  RUPTURE. 

If  the  material  of  a  beam  offered  equal  resistances  to  tension 
and  compression,  and  if  the  fibres  acted  independently  of  each 
other  in  effecting  this  resistance,  then  the  maximum  fibre  stresses, 
which  occur  at  the  top  and  bottom  of  the  beam,  could  be  readily 
calculated  as  follows: 

For  any  rectangular  section  loaded  in  the  middle  S  =  5-^-71 ', 

£  o  d 

for  a  beam  1  inch  square  and  12  inches  long,  S  =  18  W,  or  in 
general  terms  for  any  symmetrical  beam,  under  any  condition  of 


LIMITS  FOR  THE   SAFE  LOAD.  33 

8  =  maximum  fibre  stress.  w  =  load. 

6  =  breadth  of  beam.  I  =  length  of  beam. 

d  =  depth  of  beam.  M—  bending  moment. 

/  =  moment  of  inertia  about  the  neutral  axis  at  right  angles  to 
the  direction  of  pressure. 

But,  as  previously  stated,  neither  of  these  usually  assumed 
conditions  exist. 

It  seems  probable  that  the  fibres  nearer  the  axis,  by  means  of 
lateral  adhesion,  relieve  the  outer  fibres  from  a  portion  of  the 
stress  which  the  usually  accepted  theory  indicates,  and  conse- 
quently have  their  own  portion  of  the  theoretical  stress  cor- 
respondingly increased.  It  is  therefore  necessary  to  abandon  the 
deceptive  term  of  "maximum  fibre  stress,"  and  substitute  a 
"  modulus  "  determined  by  means  of  the  foregoing  formulae. 

This  modulus  will  vary  for  varying  cross-sections,  and  recent 
experiments  make  it  seem  probable  that  it  will  vary  with  the 
length  of  beam,  etc. 

The  average  of  a  large  number  of  experiments  on  standard 
flanged  beams  give  an  ultimate  modulus  of  42,000  Ibs.  On  solid 
rectangular  sections  the  modulus  will  run  higher,  or  from  45,000 
to  50,000  Ibs. 

We  adopt  42,000  as  the  modulus  for  ultimate  transverse 
strength  of  I  beams.  All  our  tables  are  calculated  by  taking 
S  —  14,000,  or  one-third  of  the  ultimate  strength  of  the  beam. 

LIMITS  FOR  THE  SAFE  LOAD. 

Inasmuch  as  there  is  a  great  diversity  in  published  tables  of 
safe  loads  for  beams,  every  one  must  judge  for  himself  what  pro- 
portion of  the  elastic  strength  of  the  beam  will  best  suit  his 
purpose. 

The  character  of  the  load  must  be  considered,  and  the  mode  of 
application  of  the  same.  If  the  load  is  suddenly  applied,  espe- 
cially if  accompanied  by  impact,  the  dynamic  stresses  resulting 
therefrom  will  not  be  expressed  by  fcrmulae  which  are  derived 
from  static  considerations  alone.  Freedom  from  vibration  or 
excessive  deflection  have  usually  to  be  provided  for,  or  the  beam 
may  be  of  considerable  length  without  lateral  support.  In  many 
such  cases  it  may  be  necessary  to  take  one-fourth  or  one-fifth  of 
the  ultimate  strength  of  the  beam  as  the  working  basis,  instead  of 
3 


34:          WROUGHT  IRON  AND  STEEL. 

one-third,  as  given  in  our  tables,  which  we  give  as  the  "  great- 
est safe  loads." 

We  have  every  confidence  in  the  accuracy  of  the  tables,  as  the 
results  of  a  number  of  careful  tests  we  have  recently  made  show 
that  very  rarely  does  the  ultimate  strength  of  the  beam  fall  below 
the  limits  we  have  given,  and  in  some  instances  it  considerably 
exceeds  those  limits. 

We  have  in  our  own  service  beams  that  are  continually  subjected 
to  much  higher  bending  stresses  than  would  be  assigned  to  them 
by  our  tables  without  any  evidence  of  a  want  of  stability. 

FACTOR  OF  SAFETY. 

For  factors  of  safety  the  following  table  will  give  results  in 
harmony  with  good  practice. 

CHARACTER  OF  STRESS.  GREATEST  SAFE  LOAD. 

Quiescent  load,  subject  to  little  or  no  vibra-  [         .1.  o£  ultimate 
tion  as  in  light  roofs,  etc.  J 

Fluctuating  loads  causing  vibration,  but") 

no  sudden  application  of  the  maximum  I          ,     „    -,,.      , 
load.     Such  as  lateral  bracing  of  bridges,  f        *  ol 
roofs  carrying  shafting,  etc.  J 

When  maximum  loads  are  suddenly  ap- 
plied. 

When  maximum  stresses  are  suddenly  re-  )          t    . 
versed  in  direction.  f         «  oi 


UNSYMMETRICAL  BEAMS. 

When  beams  have  not  an  identical  cross-section  above  and 
below  the  neutral  axis,  as  in  Deck  Beams,  Tees,  Angles,  etc., 
experiment  shows  no  substantial  difference  in  either  the  strength 
or  stiffness  of  the  beams,  whether  the  greatest  flange  is  in  ten- 
sion or  compression,  up  to  or  nearly  to  the  elastic  limit.  When 
the  least  flange  is  in  compression  the  elastic  limit  ranges  a  little 
higher  than  when  it  is  in  tension,  and  in  the  former  case,  after 
the  elastic  limit  is  passed,  the  beam  generally  exhibits  much  less 
deflection  and  higher  ultimate  resistance  than  when  loaded  with 


PENCOYD  BEAMS — GREATEST  SAFE  LOAD.  35 

the  least  flange  in  tension.     This  is  probably  due  to  the  high 
resistance  of  wrought  iron  to  crushing  after  the  elastic  limit  is 


There  are  some  exceptions  to  this,  as  in  the  case  of  very  long 
beams  that  present  no  adequate  resistance  to  lateral  flexure,  but 
as  such  cases  are  outside  the  bounds  of  good  practice  they  re- 
quire no  further  notice.  The  authoritative  formula?  most  gener- 
ally accepted  are  based  upon  a  maximum  fibre  stress  obtained  as 

follows:    S=-j-'    -3f=  bending  moment,     d  =  distance  from 

neutral  axis  to  farthest  edge  of  section.  I  =  moment  of  inertia 
about  the  axis  passing  through  the  centre  of  gravity  at  right 
angles  to  direction  of  pressure.  This  does  not  give  results  in 
harmony  with  experiments,  except  by  taking  S  as  a  modulus, 
whose  value  would  not  agree  with  that  used  for  symmetrical 
beams,  and  whose  value  would  have  to  be  derived  by  experiments 
for  differing  cross-sections.  By  taking  the  moments  of  inertia 
above  and  below  an  axis  so  located  that  the  forces  producing 
tension  and  compression  are  in  equilibrium,  and  using  the  mod- 
ulus, S  —  42,000,  as  in  symmetrical  beams,  results  harmonizing 
with  experiments  are  obtained. 

But,  for  simplicity,  we  have  adopted  the  following  methods 
for  calculating  the  safe  load,  which,  though  incorrect  in  prin- 
ciple, yet  give  correct  results  for  the  particular  sections  referred 
to. 

Deck  Beams  -g-j   =  S  =  42,000. 

Tees  and  Angles  of  equal  legs  and  )   f*_4  _  £  —  45  000. 
uniform  thickness.  f    2  / 

Notation  as  for  equal  flanged  beams. 

PENCOYD  BEAMS. 

GREATEST     SAFE    LOADS. 

The  following  tables  for  I  beams,  channels,  and  deck  beams 
give  the  greatest  safe  loads  in  net  tons,  evenly  distributed  over 
the  beams,  and  including  the  weight  of  beam  itself. 

These  loads  are  one-third  (£)  of  the  ultimate  strength  of  the 
beams,  and  are  correct  for  the  corresponding  sectional  areas 


36 


WKOUGHT   IKON   AND    STEEL. 


given.  The  several  values  are  obtained  by  the  methods  described 
on  page  88,  and  have  been  confirmed  by  numerous  experi- 
ments. The  beams,  if  of  considerable  length,  are  supposed  to 
be  braced  horizontally,  and  it  is  safest  to  limit  the  application  of 
the  tabular  loads  to  beams  whose  length  between  lateral  sup- 
ports does  not  exceed  twenty  times  the  flange  width. 

Our  experience  has  been  that  a  beam  without  lateral  support 
is  much  more  stable  than  is  commonly  supposed.  In  an  open 
webbed  beam,  the  top  flange  acts  as  a  simple  strut,  and  is  liable 
to  lateral  flexure  when  the  unsupported  length  is  considerable. 
But  in  a  solid  beam  the  parts  in  tension  sustain  the  parts  in  com- 
pression rigidly,  and  prevent  the  buckling  which  would  other- 
wise occur. 

A  number  of  careful  experiments  have  shown  a  reduction  of 
about  one-third  of  the  normal  modulus  of  rupture  when  the 
length  of  the  beam  becomes  80  times  its  flange  width.  But  as 
the  long  beam  may  suffer  if  exposed  to  accidental  cross  strains, 
we  recommend  the  greatest  safe  load  to  be  reduced  in  such  a 
ratio  for  long  beams  that  when  the  length  is  seventy  times  the 
flange  width  the  greatest  safe  loads  will  be  reduced  one-half. 
This  will  give  safe  loads,  corresponding  to  given  lengths  as  fol- 
lows: 

BEAMS   WITHOUT   LATERAL   SUPPORT. 


LENGTH    OF  BEAM. 


PROPORTION  OP  TABULAR  LOAD  FORMING 
GREATEST    SAFE  LOAD. 


20  times  flange  width. 

30      " 
40      « 

50      "        "          " 
GO      " 

70      «' 


Whole  tabular  load. 

rfc 


The  safe  loads  for  any  other  length,  not  given  in  the  tables 


DEFLECTION.  37 

can  readily  be  found  by  simple  proportion,  remembering  if  the 
span  is  very  short  to  limit  the  load  to  that  given  in  col.  xiv, 
pages 93-97,  headed  "  Maximum  load  in  tons."  If  beams  of  any 
sectional  area  not  given  in  the  tables  are  used,  the  strength  can 
be  found  as  described  on  page  106,  or  a  close  approximation  to 
the  same  by  the  rule  on  page  69. 

DEFLECTION". 

Inasmuch  as  the  elasticity  of  iron  and  steel  is  very  variable 
and  uncertain,  the  tabular  deflections  are  given  as  the  nearest 
probable,  and  are  obtained  as  described  on  page  89. 

The  tabular  deflections  correspond  to  the  given  loads  evenly 
distributed,  and  apply  to  any  sectional  area  for  each  size  of 
beams  respectively,  when  the  corresponding  loads  bear  a  uni- 
form ratio  to  the  strength  of  the  beam. 

The  greatest  safe  load  in  the  middle  of  the  beam  is  exactly 
one-half  (i)  of  the  distributed  load,  and  the  deflection  for  the 
former  will  be  eight-tenths  (y,,)  of  the  deflection  corresponding 
to  the  distributed  load  as  given  in  the  tables.  If  the  load  is 
placed  out  of  centre  on  the  beam,  it  will  bear  the  same  ratio  to 
the  load  at  the  centre  that  the  square  of  half  the  span  bears  to 
the  product  of  the  segments  of  the  beam  formed  by  the  position 
of  the  load. 

Example. — A  15-inch  200  Ib.  I  beam,  16  feet  between  sup- 
ports, will  safely  carry  an  evenly  distributed  load  (by  the  tables) 
of  26.5  tons,  and  deflect  under  same  .27  inches.  The  greatest 
safe  load  in  the  middle  will  be  one-half  the  above,  viz.,  13.25 
tons,  and  the  resulting  deflection  fa  of  the  former,  or  .22 
inches. 

If  the  weight  is  concentrated  3  feet  out  of  centre,  or  5  feet 
and  11  feet  from  the  ends,  then  the  square  of  half  the  span  being 
64,  and  the  product  of  the  segments  being  55,  the  greatest  safe 

,     ,     .,.  ,     18.25x64 

load  will  be =  15.4  tons. 

55 

If  a  beam  of  above  size  and  length  is  used  without  any  lateral 
support,  reduce  the  safe  load  in  the  ratio  aforesaid.  Thus  the 
flange  is  5$  inches  wide,  and  the  length  33  times  this ;  there- 
fore the  greatest  safe  load  will  be  a  little  less  than  •&•  of  the 
results  in  the  example. 


OS  WROUGHT   IRON   AND    STEEL. 

If  the  beam  is  exposed  to  much  vibration,  or  the  action  of 
moving  loads,  etc. ,  reduce  the  tabular  loads,  as  previously  de- 
scribed on  page  34. 

For  beams  of  other  character  than  described,  the  greatest 
safe  loads  and  corresponding  deflections  will  bear  the  following 
ratios  to  the  tabulated  loads,  for  the  same  lengths  of  beams  : 


CHARACTER  OP  BEAM. 

GREATEST  SAFE   LOAD. 

DEFLECTION. 

Fixed  at  one  end,  with  the 
load  concentrated  at  the 
other  end. 

One-eighth  (•*-)  part 
of  the  tabular 
load. 

Three  and  one- 
fifth  (8Jl)  times 
the  tabular  de- 
flection. 

Fixed  at  one  end,  with  the 
load  uniformly  distrib- 
uted. 

One-fourth  ({)  part 
of  the  tabular 
load. 

Two  and  two- 
fifths  (2|)times 
the  tabular  de- 
flection. 

Rigidly  fixed  at  both  ends, 
with  a  load  in  the  mid- 
dle of  beam. 

Same  as  the  tabu- 
lar load. 

Four-tenths  (-&) 
of  the  tabular 
deflection. 

Rigidly  fixed  at  both  ends, 
with  the  load  uniformly 
distributed. 

One    and  one-half 
(li)  times  the 
tabular  load. 

One-sixth  (£)  of 
the  tabular  de- 
flection. 

Continuous  beam  loaded  in 
middle. 

Same  as  the  tabu- 
lar load. 

Four-tenths  (-&) 
of  the  tabular 
deflection. 

Continuous  beam  load  uni- 
formly distributed. 

One   and    one  half 
(H)     times    the 
tabular  load. 

One-sixth  (£)  of 
the  tabular  de- 
flection. 

LIMIT    FOB    DEFLECTION.  39 

BEAMS    WITH  FIXED    ENDS. 

It  is  necessary  to  bear  in  mind  the  distinction  between  ends 
"rigidly  fixed"  and  ends  simply  "supported,"  the  latter  being 
the  class  contemplated  in  all  our  tables  of  safe  loads.  By 
"rigidly  fixed,"  as  denoted  in  the  previous  table,  we  mean  that 
the  beam  must  be  so  securely  fastened  at  both  ends,  by  being 
built  into  solid  masonry,  or  so  firmly  attached  to  au  adjacent 
structure,  that  the  connection  would  not  be  severed  if  the  beam 
was  exposed  to  its  ultimate  load.  In  this  case,  the  beam  is  of 
the  same  character  as  if  continuous  over  several  supports,  or 
as  if  consisting  of  two  cantilevers,  the  space  between  whose 
ends  was  spanned  by  a  separate  beam. 

CONTINUOUS  BEAMS. 

If  a  beam  is  continuous  over  several  supports,  and  is  equally 
loaded  on  each  span,  the  greatest  safe  loads  and  the  resulting 
deflections  on  any  intermediate  span  will  be  as  given  in  the  pre- 
ceding table.  But  the  end  spans  of  such  a  beam,  being  only 
semi-continuous,  must  be  either  of  a  shorter  span  than  the  in- 
termediates, or  if  of  the  same  length,  the  load  must  be  dimin- 
ished. See  ''Continuous  Beams,"  page  75. 

LIMIT    FOR    DEFLECTION. 

It  is  considered  good  practice  in  the  case  of  plastered  ceilings, 
or  in  other  circumstances  where  undue  deflection  may  be  pre- 
judicial, to  proportion  beams  so  that  their  deflection  will  not  ex- 
ceed gl0-  of  an  inch  per  foot  of  span,  or  -3£-n-  part  of  the  span. 
A  heavy  black  line  is  marked  across,  or  partly  across,  each  page. 
All  beams  below  these  lines  will  deflect  in  excess  of  this  limit; 
those  above  the  line  are  safe  to  use. 


40 


WROUGHT   IKON   AND    STEEL. 


15" 


PENCOYD 


BEAMS. 


12" 


Maximum  and  Minimum  sections  of  each  shape. 

Greatest  safe  load  in  Net  Tons  evenly  distributed,  including  beam  itself. 
Deflections  in  inches  corresponding  to  given  loads  for  each  size  of  beam. 
For  a  load  in  middle  of  beam,  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  -fa  of  the  tabular  deflection. 


CHART 
NUMBER. 

« 

1 

2 

2 

go 

- 

3 

3 

4 

4 

» 

i 

SIZE  OF  BEAM 
IN  INCHES. 

15" 

15" 

15" 

15" 

M 

12" 

12" 

12" 

12" 

|t 

WT.  PER  YD. 
IN  LBS. 

233 

200 

201 

145 

I 

1&4 

168 

163 

120 

I 

MOMENT  OF 
INERTIA. 

743.6 

682.1 

626.6 

521.2 

| 

403.5 

372.0 

324.6 

272.9 

| 

GREATEST  SAFE  LOAD. 

H 

P 

GREATEST  SAFE  LOAD. 

P 

10 

46.29 

42.44 

38.96    22.10 

11 

31.36   28.93 

25.24 

21.22 

.13 

11 

42.08 

38.58 

35.42    22.10 

13 

28.51    26.30    22.95 

19.29 

.16 

12 

38.57 

35.37 

32.47    22.10 

IB 

26.13    24.11 

21.03 

17.69    .19 

13 

35.61 

32.65 

29.97 

22.  10 

.18 

24.12 

22.25 

19.42 

16.32 

.22 

14 

33.06 

30.31 

27.83 

22.10 

21 

22.40 

20.67 

18.03 

15.16 

.26 

EH         15 

30.815 

28.29 

5>5.97j  21.62 

?4 

20.91    19.29 

16.83 

14.15 

.30 

W         16 

28.93 

26.53 

21.35 

20.  -27 

27 

19.60    18.08 

15.76 

13.26    .34 

g        17 

27.23 

24.96 

22.92 

19.08 

.30 

18.45 

17.02 

14.85 

12.48 

.38 

^        18 

25.72 

23.58 

21.64 

18.02 

34 

17.42 

16.07 

14.02 

11.79 

.43 

K         19 

24.36 

22.34 

20.51 

17.07 

38 

16.51 

15.23 

13.28 

11.17 

.48 

20 

23.14 

21.22 

19.48 

16.21 

42 

15.68 

14.47 

12.62 

10.61    .53 

§         21 

22.04 

20.21 

18.55 

15.44 

.46 

14.93 

13.78 

12.02 

10.11    .58 

OQ         22 

21.04 

19.29 

17.71 

14.74 

.51 

14.25 

13.15 

11.47 

9.65 

«4 

23 

20.13 

18.45 

16.94 

14.10 

.56 

13.63 

12.58 

10.97 

9.23 

.70 

&H        24 

19.29 

17.68 

16.23 

13.51 

.61 

13.07 

12.05 

10.52 

8.84    .77 

0         25 

18.52 

16.98 

15.58 

12.97 

.66 

12.54 

11.57 

10.10 

_8J9L83 

g        36 
g        27 

17.80 
17.14 

16.32 
15.72 

14.99 
14.43 

12.47 
12.01 

.72 

77 

12.06 
11.61 

11.13 
10.72 

9.71 
9.35 

8.16    .90 
7.86    .97 

H         28 

16.53 

15.16 

13.91 

11.58 

83 

11.20 

10.33 

9.01 

7.581.05 

S         29 

15.96 

14.63 

13.43 

11.18 

.89 

10.81 

9.98 

8.70 

7.32 

1.12 

30 

15.43 

14.15 

12.99 

10.81 

95 

10.45 

9.64 

8.41 

7.07 

1.20 

31 

14.93    13.69 

12  57i  10.46 

1  0?, 

10.12 

9.33 

8.14 

6.85 

1.28 

32 

14.47  13^6 

ira 

10.13 

l"09 

9.80 

9.04 

7.89 

6.63 

1.36 

33 

14.03    12.86 

11.81 

9.83 

1.16 

9.50 

8.76J     7.65 

6.43 

1.44 

TABLE  OF   SAFE  LOADS. 


41 


PENCOYD 


101" 


BEAMS. 


10" 


Maximum  and  Minimum  sections  of  each  shape. 

Greatest  safe  load  in  Net  Tons  evenly  distributed,  including  beam  itself. 
Deflections  in  inches  corresponding  to  given  loads  for  each  size  of  beam. 
For  a  load  in  middle  of  beam  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  y0-  of  the  tabular  deflection. 


CHART 
NUMBER. 

5 

5 

E* 

5t 

6 

6 

GC 

7 

7 

8 

8 

£ 

H 

1 

SIZE  OF 

BEAM  IN 

iot" 

iot" 

ict" 

ict" 

iot" 

ict" 

< 

10" 

10" 

10" 

10" 

INCHES. 

0 

1-1 

o 

WT.  PER 

M 

YARD  IN 

161 

134 

135 

108 

109 

89 

0 

137 

112 

106 

90 

£ 

LBS. 

fc 

92 

MOMENT 

1                 ! 

fc 

§ 

OF 

265.7 

241.6 

219.5 

195.4 

180.3 

162.3 

0 

194.4  173.6 

161.3 

148.3 

£ 

INERTIA. 

H 

H 

GREATEST  SAFE  LOAD. 

W 
fi 

GREATEST  SAFE  LOAD 

1 

10 

23.62 

21.49 

19.51 

17.37    16.03 

13.35 

.15 

18.14 

16.20 

15.08 

13.84 

.16 

11 

21.47 

19.54 

17.74 

15.79    14.57 

13.11 

.18 

16.49  14.73 

13.71 

12.58 

.19 

12 

19.68 

17.91 

16.26 

14.48    13.3H 

12.02 

.22 

16.13118.50 

12.57 

11.54 

.23 

13 

18.17 

16.53 

15.01 

13.36    12.33 

11  09 

23 

13  95  12  46 

11.60 

10.65 

.27 

14 

16.87 

15.35 

13.94 

12.41 

11.4-) 

10.30 

.30 

12.94 

11.57 

10.77 

9.89 

.3] 

15 

15.75 

14.33 

13.01 

11.58 

10.69 

9.61 

.34 

12.0910.80 

JO.  05 

9.23 

.36 

H     16 

14.76 

13.43 

12.19 

10.86 

10.02 

9.01 

.39 

11.34  10.13 

9.42 

8.65 

.41 

13.90 

12.64 

11.48 

10.22 

9.43 

8.48 

.44 

10.67 

9.53 

8.  87 

8.14 

.46 

^     18 

13.12 

11.94 

10.84 

9.65 

8.91 

8.01 

.49 

10.08 

9.00 

8.38 

7.fi9 

.52 

£     19 

12.43 

11.31 

10.27 

9.14 

8.44 

7.59 

.55 

9.55!  8.53 

7.94 

7.29 

.58 

H     20 

11  81 

10.74 

9.75 

8.69 

8.01 

7.21 

.61 

9.071  8.10 

7.E4 

6.92 

.64 

§     21 

J1.25 

10.23 

9.29 

8.27 

7.63 

6.87 

.6*! 

Tel 

T72 

TTs 

T^"S 

On 

MataMi 

mean**  t  —  ^—  • 
1 

"""" 

™" 

M     22 

10.74 

9.77 

8.87     7.90 

7.28 

6.55 

.74 

8.25 

7.36 

6.85 

6.29 

.78 

&     23 

10.27 

9.34 

8.48      7.55      6.97 

6.27 

.81 

7.89 

7.04!  6.56 

6.02 

.85 

0     24 

9.84 

8.95 

8.13     7.24     6.  68 

6.01 

.83 

7.56 

6.75!  6.28 

5.77 

.92 

K     25 

9.45 

8.60 

7.80 

6.95     6.41 

5.77 

.95 

7.26 

6.48 

6.03 

5.54 

1.00 

H 

<£     26 

9  00 

8  27 

7  51 

6  6*3      fi  16 

5  54 

1  03 

6  98 

6  23 

5  80 

5  32 

1  08 

8.75 

7.96 

7.23      6.43     5.94 

5.34 

1.11 

6.72 

6.00!  5.59 

5.13 

1.17 

3     28 

8.43 

7.67 

6.97      6.20     5.72 

5.15 

1.19 

tf.48 

5.79    5.39 

4.94 

1.26 

29 

8.14 

7.41 

6.73 

5.99      5.53 

4.97 

1.28 

6.26 

5.  59    5.20 

4.77 

1.35 

30 

7.87 

7.17 

6.51 

5.79      5.34 

4.80 

1.37 

6.05 

5.40    5.03 

4.61 

1.44 

31 

7  6" 

6  93 

6  29      5  60      5  16 

4.65 

1  46 

5  85 

5  23    4  86  1  4  47 

1  54 

32 

7.38 

6.72 

6.09      5.43      5.01 

4.50 

1.57 

5.67 

5.061  4.71 

4.33 

1.64 

33 

7.19 

6.51 

5.91 

5.26     4.86 

4.37 

1.68 

5.50 

4.91 

4.57 

4.19 

1.75 

WROUGHT  IRON  AND  STEEL. 
9" 


PENCOYD 


8" 


BEAMS. 


Maximum  and  Minimum  sections  of  each  shape. 

Greatest  safe  load  in  Net  Tons  evenly  distributed,  including  beam  itself. 

Deflection  in  incites  corresponding  to  given  loads  for  each  size  of  beam. 

For  load  in  middle  allow  one-half  the  tabular  figures. 

Deflection  for  latter  load  will  be  -jjo  of  the  tabular  deflection. 


CHART 
NUMBER. 

9 

9 

10 

10 

W 

11 

11 

12 

12 

* 

M 

< 

SIZE  OF  BEAM 
IN  INCHES. 

9" 

9" 

9" 

9" 

B 

8" 

8" 

8" 

8" 

S> 

WT.  PER  YD. 
IN  LBS. 

122 

90 

QQ 

70 

C- 

g 

00 

109 

81 

75 

65 

1 

MOMENT  OF 
INERTIA. 

143.7 

118.8 

106.8 

94.4 

o 

98.6 

£3.9 

74.5 

09.2 

1 

GREATEST  SAFE  LOAD. 

c 

p 

GREATEST  SAFE  LOAP. 

1 

6 

24.27 

16.53 

18.42 

9.94 

.06 

19.22    15.49 

14.48 

10.46 

.07 

7 

20.80 

16.53 

15.79 

9.94 

.08 

16.47;  13.99 

12.41 

10.46 

.10 

8 

18.20 

15.40 

13.81 

9.94 

.11 

14.41    12.24 

10.86 

10.08 

.13 

9 

10.18 

13.69 

12.27 

9.94 

.14 

12.81 

10.88 

9.66 

8.96 

.16 

10 

14.56 

12.32 

11.05 

9.79 

.18 

11.53 

9.79 

8.69 

8.07 

.20 

EH          11 

13.24 

11.20 

10.04 

8.90 

.22 

10.48     8.90 

7.90 

7.33 

.24 

W         12 

12.13 

10.26 

9.21 

8.16 

.26 

9.61 

8.16 

7.24 

6.72 

.29 

g        13 

11.20 

9.48 

8.50 

7.53 

.30 

8.8? 

7.53 

6.68 

6.21 

.34 

*r          14 

10.40 

8.80 

7.89 

7.00 

.35 

8.24 

6.99 

6.21 

5.76 

.39 

G         15 

9.71 

8.21 

7.37 

6.53 

.40 

7.69 

6.53 

5.79 

5.38    .45 

16 

9.10 

7.70 

6.91 

6.12 

.46 

7.21 

6.12 

5.43 

5.04    .51 

5j        17 

8.56 

7.25 

6.50 

5.76 

.52 

"T78 

T76 

-5J2 

T74 

"58 

PH 

03           18 

8.09 

6.84 

6.14 

5.44 

.58 

6.41 

5.44 

4.83 

4.48 

.65 

fa        19 

7J86 

"O8  ""f)"s2 

Tl5 

-64 

6.07 

5.15 

4.57 

4.24 

.72 

0        20 

7.28 

e!i6i   s!52 

4.90 

.71 

5.76 

4.89 

4.34 

4.03 

.80 

21 

6.93 

5.86     5.25 

4.66 

.78 

5.49 

4.66 

4.14 

3.84 

.88 

H        22 

6.62 

5.60     5.02 

4.45 

.86 

5.24 

4.45 

3.95 

3.07 

.97 

£        23 

6.33 

5.8o|     4.80 

4.25 

.94 

5.01 

4.25 

3.78 

3.50 

1.06 

W        24 

6.07 

5.13!    4.61 

4.08 

1.02 

4.80 

4.08 

3.62 

3.36 

1.16 

K;        25 

5.82 

4.93     4.42 

3.92 

1.11 

4.61 

3.91 

3.48 

3.22 

1.26 

26 

5.60 

4.74     4.25 

3.77 

1.21 

4.43 

3.77 

3.34 

3.10 

1.36 

27 

5.39 

4.561     4.09 

3.631.30 

4.27 

3.62 

3.22 

2.98 

1.46 

28 

5.20 

4.40     3.95 

3.50  1.40 

4.12 

3.50 

3.10 

2.88 

1.57 

29 

5.02 

4.25 

3.81 

3.381.50 

3.98 

3.37 

3.00 

2.78 

1.68 

TABLE   OF  SAFE  LOADS. 


7" 


PENCOYD 


6" 


BEAMS. 


Greatest  safe  load  in  Net  Tons  evenly  distributed,  including  beam  itself. 
Deflections  in  inches  corresponding  to  given  loads  for  eacli  size  of  beam. 
For  a  load  in  middle  of  beam  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  ^o  of  the  tabular  deflection. 


CHART 
NUMBER. 

13 

13         14 

14 

05 
1 

15 

15 

16 

16 

5 

SIZE  OF  BEAM 
IN  INCHES. 

7" 

7" 

7" 

7" 

M 
i- 

6" 

6" 

6" 

6" 

H 

WT.  PER  YD. 
IN  LBS. 

88 

75 

63 

51 

i 

to 

63 

55 

48 

40 

1 

(0 

MOMENT  OF 
INERTIA. 

58.6 

53.3 

48.0 

43.1 

O 

30.8 

27.5 

26.3 

24.1 

O 
1 

3 

3 

E 

E 

GREATEST  SAFE  LOAD. 

ft 

GREATEST  SAFE  LOAD. 

1 

6 

12.93 

11.75 

10.65 

6.17 

.08 

8.03 

7.42 

6.87 

6.25 

.10 

7 

11.09 

10.07 

9.13 

6.17 

.11 

6.89 

6.36 

5.89 

5.36 

.13 

8 

9.70 

8.81 

7.99 

6.17 

.15 

6.02 

5.56 

5.15 

4.C9 

.17 

9 

8.62 

7.83 

7.10 

6.17 

.19 

5.36 

4.94 

4.58 

4.17 

.22 

10 

7.76 

7.05 

6.39 

5.74 

.23 

4.82 

4.45 

4.12 

3.74 

.27 

^        11 

7.05 

6.41 

5.81 

5.22 

.28 

4.38 

4.05 

3.75 

3.41 

.32 

H         12 

6.47 

5.87 

5.32 

4.79 

.33 

4.02 

3.71 

3.43 

3.12 

.38 

g         13 

5.97 

5.42 

4.92 

4.41 

.38 

T77 

nra 

TIT 

T^ 

"43 

fc         14 

5.54 

5.04 

4.56 

4.10 

.44 

3.44 

3.18 

2.94 

2.68 

.52 

15 

TTT 

"4*70 

T38 

-O 

"51 

3.21 

2.97 

2.75 

2.50 

.60 

fc         16 

4.85 

4.41 

3.99 

3.59 

.58 

3.01 

2.78 

2.57 

2.34 

.69 

<5        17 

4.5(3 

4.15 

3.76 

3.38 

.66 

2.84 

2.62 

2.42 

2.21 

.78 

PH 

60        18 

4.31 

3.92 

3.55 

3.19 

.74 

2.68 

2.47 

2.29 

2.08 

.87 

fc         19 

4.08 

3.71 

3.36 

3.0-2 

.82 

2.54 

2.34 

2.17 

1.97 

.97 

0        20 

3.88 

3.52 

3.19 

2.87 

.90 

2.41 

2.22 

2.06 

1.87 

1.07 

21 

3.70 

3.36 

3.04 

2.73 

.99 

2.30 

2.12 

1.96 

1.78 

1.18 

M 

EH           0-2 

3.53 

3.20 

2.90 

2.61 

1.09 

2.19 

2.02 

1.87 

1.70 

1.29 

S         23 

3.37 

3.07 

2.77 

2.491.20 

2.10 

1.93 

1.79 

1.63 

1.41 

g        24 

3.23 

2.94 

2.66 

2.39  1.33 

2.01 

1.85 

1.72 

1.  5611.54 

3        25 

3.10 

2.82 

2  56 

2.30 

1.43 

1.93 

1.78 

1.65 

1.50 

1.67 

26 

2.98 

2.71 

2.46 

2.21 

1.55 

1.85 

1.71 

1.58 

1.44 

1.81 

27 

2.87 

2.61 

2.37 

2.121.67 

1.78 

1.65 

1.53 

1.39,1.95 

28 

2.77 

2.52 

2.28 

2.051.80 

1.72 

1.59 

1.47 

1.34  2.10 

29 

2.68 

2.43 

2.20 

1.981.93 

1.66 

1.53 

1.42 

1.2912.25 

44 


WROUGHT   IRON   AND    STEEL. 


5" 


PENCOYD 


BEAMS. 


4" 


Greatest  safe  load  in  Net  Tons  evenly  distributed,  including  beam  itself. 
Deflections  in  inches  corresponding  to  given  loads  for  each  size  of  beam. 
For  a  load  in  middle  of  beam  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  •&  of  the  tabular  deflection. 


CHART 
NUMBER. 

17 

17 

18 

18 

oc 

• 
1 

19 

19 

20. 

20. 

ai 

m 

SIZE  OF  BEAM 
IN  INCHES. 

5" 

5"        5" 

5" 

~ 

H 

is 

4" 

4"    |    4" 

4" 

w 
« 

Tj< 

WT.  PER  YD. 
IN  LBS. 

40 

36         33 

30 

M 

tt 

38         28 

21.5 

18.5 

03 

^ 

MOMENT  op 
INERTIA. 

14.7 

13.7 

13.1 

12.5 

LECTIO! 

9.0 

7.7 

5.5 

5.1 

O 

GREATEST  SAFE  LOAD. 

h 

a 
P 

GREATEST  SAFE  LOAD. 

W 
ft 

4 

6.80 

6.42 

6.12 

4.86 

.05 

5.25 

4.47     3.27 

3.00 

.06 

5 

5.44 

5.14 

4.90 

4.67 

.08 

4.25 

3.58 

2.6-2 

2.40.   .10 

6 

4.53 

4.28 

4.08 

3.89 

.12 

3.50 

2.98 

2.18 

2.00 

.14 

7 

3.89 

3  67 

3.50 

3.33 

.16 

3.00 

2.56 

1.86 

1.71 

.20 

8 

3.40 

3.21 

3.06 

2.92 

.21 

2.62 

2.24 

1.64 

1.50 

.28 

FH            9 

3.02 

2.86 

2.72 

2.59 

.26 

~33 

i.yy    1.46 

TB 

-33 

H         10 

2.72 

2.57 

2.45 

2.33 

.32 

2.10 

1.79 

1.31 

1.20 

.40 

§         11 

—7 

TM 

"T23 

"TT2 

"39 

1.91 

1.63 

1.19 

1.09 

.49 

K        12 

2.27 

2.14 

2.04 

1.94 

.46 

1.75 

1.49 

1.09 

1.00 

.58 

M         13 

2.09 

.98 

.88 

1.79 

.54 

1.62 

1.88 

1.01 

.92 

.68 

fc         H 

1.94 

.84 

.75 

1.67 

.63 

1.50 

1.28 

.94 

86 

.79 

3         15 

1.81 

.71 

.63 

1.55 

.72 

1.40 

1.19 

.87 

80 

.91 

OH 

50         16 

.70 

.61 

.53 

1.46 

.82 

1.31 

1.12 

.82 

.75 

1.03 

EC,        17 

.60 

.51 

.44 

1.37 

.93 

1.23 

1.05 

.77 

.71  1.17 

18 

.51 

.43 

.36 

1.30 

1.04 

1.17 

.1)9 

.73 

.671.31 

19 

.43 

.35 

.29 

1.23 

1.16 

1.11 

.94 

.69 

.631.48 

PS 

20 

.36 

.28 

.22 

1.17 

1.29 

1.05 

.89 

.65 

.60 

1.61 

25        21 

.29 

.22 

.17 

1.11  1.42 

1.00 

.85 

,6'2 

.571.77 

§        23 

.24 

.17 

.11 

l.Olil.58 

.95 

.81 

.60 

.541.93 

3        23 

.18 

.12 

.07 

1.01 

1.70 

.91 

.78 

.57 

.522.12 

24 

.13 

1.07 

1.02 

.97 

1.85 

.87 

.75 

.55 

.50,2.32 

25 

.09 

1.03 

.98 

.93  2.01 

.84 

.7-2 

.52 

.48^2.51 

26 

.04 

.99 

.94 

.902.18! 

.81 

.69 

.50 

.46  2.71 

27 

1.01 

.95 

.91 

.86 

2.36 

.78 

.66 

.48 

.44 

2.91 

TABLE   OF   SAFE   LOADS. 


45 


PENCOYD 


BEAMS. 


Maximum  and  Minimum  sections  of  each  shape. 

Greatest  safe  load  in  Net  Tons  evenly  distributed  including  beam  itself. 
Deflections  in  inches  corresponding  to  given  loads  for  each  size  of  beam. 
For  a  load  in  middle  of  beam  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  'nT  of  the  tabular  deflection. 


CHART 
NUMBER. 

21 

21 

22 

22 

a 

SIZE  OP  BEAM 
IN  INCHES. 

3" 

3" 

3" 

3" 

| 

WT.  PER  YD. 
IN  LBS. 

28.6 

23 

21.7 

17 

2 

OB 

MOMENT  op 
INERTIA. 

4.0 

3.3 

3.0 

2.7 

I 

GREATEST  SAFE  LOAD. 

1 

4 

2.87 

2.56 

2.34 

2.07 

.09 

5 

2.30 

2.05 

1.87 

1.88 

.14 

6 

1.92 

1.71 

1.56 

1.38 

.19 

7 

-1-64 

HT1& 

"T34 

-n§ 

"26 

&3          8 

1.44 

1.28 

1.17 

1.03 

.34 

fe          9 

1.28 

1.14 

1.04 

.92 

.43 

^      10 

1.15 

1.02 

.94 

.82 

.53 

S       11 

1.04 

.93 

.85 

.75 

.65 

fc        12 

.96 

.85 

.78 

.69 

.77 

^         13 
§3         14 
15 

.88 
.82 
.77 

.79 
.73 

.68 

.72 
.67 
.62 

.64 
.59 
.55 

.91 

1.05 
1.21 

C        16 

17 
g        18 

| 

.64 
.60 
.57 

.58 
.55 
.52 

.521.37 
.491.55 
.4611.74 

g         19 

.61 

.54 

.49 

.44 

1.93 

W        20 

.58 

.51 

.47 

.41 

2.13 

•^        21 

.55 

.49 

.45 

.39 

2.37 

22 

.52 

.47 

.43 

.38 

2.62 

23 

.50 

.44 

.41 

.36 

2.88 

46 


WROUGHT  IKON  AND   STEEL. 


PENCOYD 


15" 


CHANNELS. 


12" 


Maximum  and  Minimum  sections  of  each  shape. 

Greatest  safe  load  in  Net  Tons  evenly  distributed,  including  beam  itself. 
Deflections  in  inches  corresponding  to  given  loads  for  each  size  of  channel. 
For  a  load  in  middle  of  beam,  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  -fa  of  the  tabular  deflection. 


CHART 
NUMBER. 

30 

30 

$ 

w 

31 

31 

32 

32 

w 

SIZE  OF  CHAN- 
NEL IN  INS. 

15" 

15" 

fc 
BE 

12" 

12" 

12" 

12" 

3 

WT.  PER  YD. 
IN  LBS. 

204.5 

148 

K 

160 

88.5 

101.5 

60 

1 

8 

§ 

g 

MOMENT  OF 
INERTIA. 

557.4 

451.5 

CO 

'EH 

g 

268.5 

182.7 

173.5 

123.7 

03 

GREATEST  SAFE  LOAD. 

1 

GREATEST  SAFE  LOAD. 

d 
1 

10 

34.68 

28.09 

.11 

20.88 

14.21 

13.  4C 

9.14 

.13 

11 

31.53 

25.54 

.13 

18.98 

12.!I2!   12.26 

8.75 

.16 

12 

28.90 

23.41 

.15 

17.40 

11.84:   11.24 

8.02 

.19 

13 

26.  63 

21.61 

.18 

16.06 

10.93    10.38 

7.40 

.22 

14 

24.77 

20.08 

.21 

14.91 

10.15     9.64 

6.87 

.26 

EH         15 

23.12 

18.73 

.24 

13.1(2 

9.47i     8.99 

6.41 

.30 

W         16 

21.68 

17.56 

.27 

13.05 

8.88 

8.43 

6.01 

.34 

g        17 

20.40 

16.52 

.30 

12.28 

8.36 

7.94 

5.66 

.38 

!z        18 

19.27 

15.61 

.34 

11.60 

7.89 

'  7.49 

5.34 

.43 

B        19 

18.25 

It.  78 

.38 

10.99 

7.48 

7.10 

5.06 

.48 

20 

17.34 

14.04 

.43 

10.44 

7.10 

6.74 

4.81 

.53 

5        21 

16.52 

13.38 

.47 

9.94 

6.77 

6.42 

4.58 

.58 

OQ        22 

15.76 

12.77 

.52 

9.49 

6.46 

6.13 

4.37J  .64 

23 

15.08 

12.21 

.57 

9.08 

6.18 

5.87 

4.18i   .70 

PM         24 

14.45 

11.70 

.62 

8.70 

5.92 

5.62 

4.01    .77 

0         25 

13.87 

11.24 

.67 

8.35 

_5.(i8 

5.40 

3.85 

.83 

g        36 

13.34 

10.80 

.73 

8M 

5.47 

5.19 

3.70 

.90 

O        27 

12.85 

10.40 

78 

7.73 

5.26 

5.00 

3.56 

.97 

§        28 

12.39 

10.03 

84 

7.46 

5.07 

4.82 

3.44  1  05 

3        29 

11.96 

9.69 

.90 

7.20 

4.90 

4.65 

3!32lll2 

30 

11.56 

9.36 

.96 

6.96 

4.74 

4.50 

3.21,1.20 

31 

11.19 

9.06 

1.03 

6.74 

4.58 

4.35 

3.101.28 

32 

TOl 

"T78 

^^^ 

^"^™ 

iTo 

6.52 

4.44 

4.22 

3.0111.36 

33 

10.51 

8.51 

1.17 

6.33 

4.31 

4.09 

2.921.44 

TABLE   OF  SAFE  LOADS. 


47 


PENCOYD 


10" 


CHANNELS. 


9" 


Maximum  and  Minimum  sections  of  each  shape. 

Greatest  safe  load  in  Net  Tons  evenly  distributed,  including  beam  itself. 
Deflections  in  inches  corresponding  to  given  loads  for  each  size  of  channel. 
For  a  load  in  middle  of  beam  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  -j80-  of  the  tabular  deflection. 


CHART 
NUMBER. 

34 

34 

35 

35 

H 

& 

36 

36 

37 

37 

i 

SlZEOFCHAN- 
NEL  IN  INS. 

10" 

10" 

10" 

10" 

<! 

9" 

9" 

9" 

9" 

CHANN 

WT.  PER  YD. 
IN  LBS. 

106 

60 

86.5 

49 

O 
B9 

93 

54 

61 

37 

* 

P 

p 

MOMENT  op 
INERTIA. 

131.0 

92.7 

105.2 

73.9 

HH 

90.7 

64.3 

59.8 

43.6 

fe 

jn 

GREATEST  SAFE  LOAD. 

M 

GREATEST  SAFE  LOAD. 

I 

10 

12.23 

8.65 

9.81 

6.89 

.16 

9.41 

6.67 

6.21     4.52 

.18 

11 

11.12 

7.86 

8.92 

6.26 

.19 

8.55 

6.  re 

5.65     4.11 

.22 

12 

10.19 

7  21 

8.17 

5.74 

.23 

7.84 

5.56 

5.17     3.77 

.28 

13 

9.41 

6^65 

7.55 

5.30 

.27 

7.24 

5.13 

4.78 

3.48 

.30 

14 

8.74 

6.18 

7.01 

4.92 

.31 

6.72 

4.76 

4.44 

3.23 

.35 

E-i        15 

8.15 

5.77 

6.54 

4.59 

.36 

6.27 

4.45 

4.14     3.01 

.40 

g         16 

7.64 

5.41 

6.13 

4.31 

.41 

5.88 

4.17 

3.88     2.82 

.46 

7.19 

5.09 

5.77 

4.05 

.46 

5.53 

3.92 

3.65,     2.66 

.52 

&        18 

6.79 

4.81 

5.45 

3.83 

.52 

5.23 

3.71 

3.45     2.51 

.58 

19 

£        20 

6.44 

6.11 

4.55 
4.32 

5.16 
4.90 

3.63 

3.44! 

.58 
.641 

T95 
4.70 

"TsT 

3.34 

3.27  TT38 
3.10     2.26 

TB 

.71 

5.82 

Tl2 

Te? 

•fa™ 

4.48 

3.18 

2.96     2.15 

.78 

00        22 

5.56 

3.93 

4.46 

3.131   .78 

4.28     3.03 

2.S2 

2.05 

.86 

fe        23 

5.32 

3.76 

4.27 

2.99 

.85 

4.09     2.90 

2.70 

1.97 

0         24 

5.10 

3.60 

4.09 

2.87 

.92 

3.92     2.78 

2.59 

1.88 

l!02 

M         25 

4.89 

3.46 

3.92 

2.761.00 

3.76      2.67 

2.48 

1.81 

1.11 

g         o6 

rh         26 

4.70 

3.33 

3.77 

2.65 

1.C8 

3.62 

2.57 

2.39 

1.74 

1.21 

fc         27 

4.53 

3.20 

3.63 

2.55  1.17 

3.49 

2.47 

2.30 

1.67 

1.30 

W        28 

4.37 

3.09 

3.50 

2.461.26 

3.36 

2.38 

2.22 

1.61 

1.40 

^        29 

4.22 

2.98 

3.38 

2.38  1.35 

3.24 

2.30 

2.14 

1.56 

.50 

30 

4.08 

2.88 

3.27 

2.301.45 

3.14 

2.22 

2.07 

1.51 

.61 

31 

3.94 

2.79 

3.16 

2.221.55 

3.03!     2.15 

2.00      1.46 

1.72 

32 

3.82 

2.70 

3.07 

2.151.65 

2.94 

2.08 

1.94!     1.41 

1.83 

33 

3.71 

2.62 

2.97 

2.09 

1.76 

2.85 

2.02 

1.88 

1.37 

1.95 

48 


PENCOYD 


WROUGHT   IRON  AND   STEEL, 

8" 


CHANNELS. 


Maximum  and  Minimum  sections  of  each  shape. 

Greatest  safe  load  in  Net  Tons  evenly  distributed,  including  beam  itself. 
Deflection  in  inches  corresponding  to  given  loads  for  each  size  of  channel. 
For  load  in  middle  of  beam  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  -ur  of  the  tabular  deflection. 


CHART 
NUMBER. 

38 

38 

39 

39 

£? 

40 

40 

41 

41 

* 

SlZEOFCHAN- 
NEL  IN  INS. 

a 
o 

7" 

7" 

7" 

7" 

I 

8'' 

8" 

8" 

8" 

WT.  PER  YD. 
IN  LBS. 

80.5 

43 

54 

30 

00 

(6 

73 

41 

49 

26 

\ 

MOMENT  OF 
INERTIA. 

60.0 

40.0 

41.0 

28.2 

to 

O 

h 

42.6 

29.5 

27.9 

18.5 

00 

GREATEST  SAFE  LOAD. 

1 

GREATEST  SAFE  LOAD. 

\ 

<3 

n 

1 

6 

11.67 

7.77 

7.93 

4.79    .07 

9.45     6.55 

6.18 

3.42 

.08 

7 

10.00 

6.66 

6.83 

4.70    .10 

8.10     5.61 

5.30 

3.42 

.11 

8 

8.75 

5.83 

5.97 

4.11     .13 

7.09     4.91 

4.64 

3.07 

.15 

9 

7.78 

5.18 

5.31 

3.6«    .16 

6.30     4.37 

4.12 

2.73 

.19 

10 

7.00 

4.66 

4.78 

3.29    .20 

5.67,    3.93 

3.71 

2.46 

.23 

gll 

6.36 

4.24 

4.35 

2.99    .24 

5.15     3.57 

3.37 

2.24 

.28 

1-2 

5.83 

3.88 

3.98 

•2.74    .29 

4.72      3.27 

3.09 

2.05 

,33 

g         I3 

5.38 

3.  58 

3.67 

2.53 

.34 

4.36      3.02 

2.85 

1.89 

.38 

£        14 

5.00 

3.33 

3.41 

2.35 

.39 

4.05     2.81 

2.65 

1.76 

.45 

"-'         15 

4.67 

3.11 

3.19 

2.19 

.45 

~3"78"T62 

"T47 

T64 

T2 

>-T         16 

4.37 

2.91 

2.99 

2.06 

.51 

3.54     2.46 

2.32 

1.54 

.59 

<        17 

-os 

"Tr4 

T8I 

HT4 

-58 

3.34      2.31 

2.18 

1.45 

.67 

*        18 

3.89 

2.59 

2.66 

1.83 

.65 

3.15 

2.18 

2.06 

.37 

.75 

fr         19 

3.68 

2.45 

2.52 

1.73 

.72 

2.98      2.07 

1.95 

.29 

.83 

0         20 

3.50 

2.33 

2.39 

1.64 

.80 

2.83      1.96 

1.85 

.23 

.92 

21 

3.33 

2.22 

2.  £8 

1.57 

.88 

2.70      1.87 

1.77 

.17 

1.01 

E-|         2° 

3.18 

2.12 

2.17 

1.50 

.97 

2.58      1.79 

1.69 

.121.11 

i        2:i 

3.04 

2.03 

2.08 

1.43 

1.06 

2.47      1.71 

1.61 

.071.22 

W         24 

2.92 

1.94 

1.99 

1.37 

1.16 

2.36      1.64 

1.55 

.021.34 

H;      25 

2.80 

1.86 

1.91 

1.32 

1.26 

2.27J     1.57 

1.48 

.98jl.45 

26 

2  61 

1.79 

1.84 

1.26 

1.36 

2.18 

1.51 

1.43 

.95'l.57 

27 

2.59 

1.73 

1.77      1.22 

1.46 

2.10      1.46 

1.37 

.91J1.69 

28 

2.50 

1.66 

1.71      1.17 

1.57 

2.02      1.40 

1.32 

.88  1.82 

89 

2.41 

1.61 

1.65 

1.13 

1.68 

1.95 

1.35 

1.28 

.851.95 

TABLE   OF   SAFE   LOADS. 


PENCOYD 


H       5"  and  6"     jl 


3"  and  4" 


CHANNELS. 


Maximum  and  Minimum  sections  of  each  shape. 

Greatest  safe  load  in  Net  Tons  evenly  distributed  including  beam  itself. 
Deflections  in  inches  corresponding  to  given  loads  for  each  size  of  chanm* 
For  a  load  in  middle  of  beam  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  TJ  of  the  tabular  deflection.  • 


CHART 
NUMBER. 

3 

42 

44 

45 

46 

M 

g 

47 

48 

49 

49 

1 

W 

£ 

SIZE  OF  ! 

\ 

* 

*• 

CHANNEL 
IN  INS. 

I 

6" 

6" 

5" 

5" 

3 

5 

5 

~WT.  PER 

^ 

* 

cb 

YD.  IN 

«b 

33.0 

23 

27 

18.8 

o 

r* 

21.5 

17.5 

18.9 

15.2 

g 

LBS. 

o 

— 

£ 

PH 
0 

fr 

MOM.  OF 
INERTIA. 

1 

18.4 

11.7 

10.3 

6.7 

fe 

fc 

5.2 

4.1 

2.3 

2.0 

1 

3 

1 

GREATEST  SAFE  LOAD. 

K 

K 
ft 

ft 

GREATEST  SAFE  LOAD. 

ft 

.02 

6.50 

5.24 

5.92 

4.13 

.02 

.03 

4.03     3.20 

2.40 

2.10 

.05 

4 

.04 

6.50 

4.54 

4.80 

3.10 

.05 

.06 

3.02,    2.40 

1.80 

1.57 

.09 

5 

.07 

5.70 

3.63 

3.84 

2.48 

.08 

.10 

2.42     1.92 

1.44 

1.26 

.14 

FH'        6 

.10 

4.75 

3.02 

3.20 

2.07 

.12 

.14 

2.02 

1.60 

1.20 

1.05 

/L9 

&3       7 

.13 

4.07 

2.59 

2.74 

1.77 

.16 

.20 

1.73 

1.37 

1.03 

.90 

.26 

^       8 

.17 

3.56 

2.26 

2.40 

1.55 

.21 

.2* 

1.511     1.20 

.90 

.79 

.34 

Y-r            9 

.22 

3.17 

2.01 

2.13 

1.38 

.26 

O)7 

.80 

.70 

.43 

K      10 

.27 

2.85 

1.81 

1.92 

1.24 

.32 

.40 

1.21 

.96 

.72 

.63 

.53 

%    n 

.32 

2.59 

1.64 

1.74 

1.13 

.39 

.49 

1.10 

.87 

.65 

.57 

.65 

PH      12 

.38 

2.37 

1.51 

1.60 

1.03 

.46 

.58 

1.01 

.80 

.60 

.52 

.77 

W      13 

"45 

2.19 

""7^J9 

1.48 

.95 

.54 

.68 

.93 

.74 

.?5 

.48 

.91 

fe      14 

.52 

2.04 

i!s3 

1.37 

.89 

.63 

.79 

.86 

.69 

!51 

.45 

1.05 

C 

15 

.60 

1  90 

1.21      1.28 

.83!    .72 

.91 

.81 

.64 

.48 

.42 

1.21 

5     16 

.69 

1.78 

1.13      1.20 

.77    .82 

1.03 

.76 

.60 

.45 

.39 

1.37 

g     17 

.78 

1.H8 

1.06      1.13 

.73    .93 

1.17 

.71 

.56 

.42 

.37 

1.55 

|     18 

.87 

1.58 

1.01 

1.07 

.691.04 

1.31 

.67 

.53 

.40 

.35 

1.74 

^     19 

.97 

1.50 

.95 

1.01 

.651.16 

1.46 

.64 

.n 

.38 

.33 

1.93 

20 

1.07 

1.42 

.90        .96 

.621.29 

1.61 

.60 

.48 

.36 

.31 

2.13 

21 

1.18 

1.36 

.86!       .91 

.591.421  1.77 

.58 

.46!       .34 

.SO 

2.37 

22 

1.29;     1.30 

.82        .87 

.56  1.56 

1.93 

.55 

.44 

.33 

.29 

2.62 

23 

1.41 

1.24 

.79        .83 

.541.70 

2.12 

.53 

.42 

.31 

.27 

2.88 

24 

1.54 

1.19 

.75        .80 

.52  1.85  12.32 

50 

.40 

.30 

26 

3.11 

25 

1.67 

1.14 

.72        .77 

.502.01  2.51 

.48 

.38 

.29 

.25 

3.34 

26 

1.81 

1.101       .70        .74 

.482.18 

1 

2.71 

•   .47 

.37 

.28 

,24 

3.50 

WKOUGHT   IRON   AND   STEEL. 


PENOOYD 


12"  and  11" 


BEAMS. 


10"  and  9" 


Maximum  and  minimum  sections  of  each  shape. 

Greatest  safe  load  in  Net  Tons  evenly  distributed,  including  beam  itself. 
Deflections  in  inches  corresponding  to  given  loads  for  each  size  of  beam. 
For  a  load-in  middle  of  beam  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  W  of  the  tabular  deflection. 


CHAUT 

NUMBER. 

* 

60 

60         61 

61 

fi 

1 

oo 

62 

62 

63 

63 

m 

g 

SIZE  OF 

H 

M 

PQ 

PQ 

BEAM  IN 

PQ 

12" 

12" 

11" 

11" 

10" 

10" 

9" 

9" 

s 

INCHES. 

fe 

£ 

o 

os 

WT.  PER 

'K 

a 

a 

M 

YD.  IN 

o 

138 

104 

118 

91 

I 

I 

105 

80 

94 

72 

fe 

LBS. 

OQ 

1 

MOM  OF. 
INERTIA. 

O 

264.9 

222.0 

193.1 

164.1 

o 

H 

140.4 

118.2    99.5 

84.8 

g 

w 

w 

W 

1 

w 

K 

i 

i 

h 

s 

GREATEST  SAFE  LOAD. 

H 
ft 

H 
ft 

GREATEST  SAFE  LOAD. 

ft 

10 

.13 

20.59 

17.26 

16.41 

13.95 

.15 

.16 

13.11 

11.03    10  32 

8.79 

.18 

11 

.16 

18.72 

15.69 

14.92 

12.68 

.18 

.19 

11.92 

10.031     9.38 

7.99 

.22 

12 

.19 

17.16 

14.38 

13.67 

11.62 

.21 

.23 

10.92 

9.19 

8.60 

7,32 

.26 

13 

.22 

1J.84 

13.28 

12.62 

10.73 

.25 

.27 

10.08 

8.48 

7.94 

6.76 

.30 

14 

.26 

14.71 

12.33 

11.72 

9.96 

.29 

.31 

9.36 

7.88 

7.37 

6.28 

.35 

.     15 

.30 

13.73 

11.51 

10.94 

9.30 

.36 

8.74 

7.35 

6.88 

5.86 

.40 

B     17 

34 

12.87 

10.79 

10.26 

8.72 

^39 

.41 

8.19 

6.89 

6.45 

5.49 

.47 

.38 

12.11 

10.15 

9.65 

8.21 

.44 

.46 

7.71 

6.49 

6.07 

5.17 

.53 

s 

18 

.44 

11.44 

9.59 

9.12 

7.75 

.49 

.52 

7.28 

6.13 

5.73 

4.88 

.59 

5     19 

49 

10.84 

9.08 

8.64 

7.34 

.54 

.58     6.90 

5.81 

4.6.3 

"65 

20 

!54 

10.29 

8.63 

8.20 

6.97 

.59 

.64 

6.55 

5.51 

5!l6 

4.39 

.72 

*     21 

.59 

9.80 

8.22 

7.81 

6.64 

.65 

6.24 

-ns 

4.91 

4.19 

.79 

§2     22 

.65 

9.36 

7.8r> 

7.46 

6.34 

.71 

.78 

5.  90 

5.01 

4.69 

4.00 

.87 

&  s 

.71 

8.95 

7.50 

-7-15 

"77 

.86 

5.70 

4.80 

4.49 

3.82 

.95 

o    ** 

.78 

8.58 

7.19 

6.84 

s!si 

.84 

.93 

5.46 

4.60 

4.30 

3.661.04 

25 

w 

"84 

"is 

6.90 

6.56 

5.58 

.91 

1.01 

5.24 

4.41 

4.13 

3.52 

1.13 

.92 

7.92 

6.64 

6.31 

5.37 

.99 

1.09 

5.04 

4.24 

3.97 

3.38 

1.23 

^     27 

.99 

7.63 

6.39 

6.08 

5.17 

1  07 

1.18 

4.86 

4.09 

3.82 

3.261.32 

«     ™ 

1.07 

7.35 

6.16 

5.88 

4.98 

1.15 

1.27 

4.68 

3.94 

3.69 

3.141.42 

i-J     29 

1.14 

7.10 

5.95 

5.66 

4.81 

1.23 

1.38 

4.52 

3.80 

3.56 

3.03 

1.52 

30 

1.22 

6.86 

5.75 

5.47 

4.65 

1.32 

1.45 

4.37 

3.67 

3.44 

2.93 

1.65 

31 

1.30 

6.64 

5.57 

5.29 

4.50 

1.41 

1.55 

4.23 

3.56 

3.33 

2.84 

1.77 

32 

1.33 

6.43 

5.39 

5.13 

4.36 

1.50 

1  65 

4.10 

3.45 

3  22 

2.751.90 

33 

1.46 

6.24 

5.23 

4.97 

4.23 

1.60  1.76 

II 

3.97 

3.34 

3.13 

2.66 

2.03 

TABLE   OF   SAFE   LOADS. 


51 


PENCOYD 


8"  and  7" 


6"  and  5" 


O 


BEAMS. 


Maximum  and  minimum  sections  of  each  shape. 

Greatest  safe  load  in  Net  Tons  evenly  distributed,  including  beam  itself. 
Deflections  in  inches  corresponding  to  given  loads  for  each  size  of  beam. 
For  a  load  in  middle  of  beam  allow  one-half  the  tabular  figures. 
Deflection  for  latter  load  will  be  -*o~  of  the  tabular  deflection. 


CHART 
NUMBER. 

i 

64 

64 

65 

65 

A 

i 

•< 

X 
•< 

66 

66 

67 

67 

•4 

SIZE  OF 
BEAM 

w 

8" 

8" 

7" 

7" 

M 

w 

M 

6" 

6" 

5" 

5" 

m 

M 

IN  IN*. 

So 

£_ 

«b 

io 

WT.  PER 

a 

ff 

6S 

K 

YD.  IN 

84 

61 

72 

52 

O 

o 

57 

42 

46 

34 

g 

LBS. 

* 

m 

3B 

MOM.  OF 
INERTIA. 

o 

70.5 

57.7 

42.6 

34.4 

I 

ECTION 

26.5 

22.0 

14.5 

12.0 

55 
O 

ft 

GREATEST  SAFE  LOAD. 

1 

U 

ft 

GREATEST  SAFE  LOAD. 

M 
ft 

6 

.07 

19.53 

11.22 

9.43 

7.63 

.08 

.10 

6.87 

5.70 

4.53 

3.73 

.12 

7 

.10 

in.  74 

9.61 

8.09 

6.54 

.11 

.13 

5.89 

4.89 

3.89 

3.20 

.16 

8 

.13 

14.65 

8.41 

7.07 

5.73 

.15 

.17 

5.15 

4.27 

3.40 

2.80 

.21 

.16 

13.02 

7.48 

6.29 

5.09 

.19 

.22 

4.58 

3.02 

2.49 

.26 

&q     10 

.20 

11.72 

6.73 

5.66 

4.58 

.23 

27 

4.12 

3.42 

2.72 

2.24 

.32 

fe     11 

24 

10.65 

6.12 

5.15 

4.16 

.28 

.32 

3.75 

3.11 

-2-47 

"T04 

-39 

.29 

9.77 

5.61 

4.72 

3.82 

.33 

.38 

3.43 

2.85 

2.27 

1.87 

.46 

B     13 

.34 

9.01 

5.18 

4.35 

3.52 

.38 

"45 

"Or 

2.63 

2.09 

1.72 

.54 

5     14 

.39 

8.37 

4.81 

4.04 

3.27 

.45 

.52 

2.94 

2.44 

1.94 

1.60 

.63 

eu    15 

.45 

7.81 

4.49 

-3T7 

"Tos 

T2 

.60 

2.75 

2.28 

1.81 

.49 

.72 

™     16 

.51 

7.33 

4.21 

3.54 

2.86 

.59 

.69 

2.57 

2.14 

1.70 

1.40 

82 

&.     17 

"58 

6.89 

"^96 

3.33 

2.69 

.67 

.78 

2.42 

2.01 

1.60 

.32 

.93 

C 

18 

.65 

6.51 

3.74 

3.14 

2.54 

.75 

.87 

2.29 

1.90 

.51 

.24 

1.04 

g     19 

.72 

6.17 

3.54 

2.98 

2.41 

.83 

.97 

2.17 

1.80 

.43 

.18 

1.16 

0     pO 

.80 

5.86 

3.36 

2.83 

2.29 

.92 

1.07 

2.06 

1.71 

.36 

.12 

1.29 

.88 

5.58 

3.20 

2.69 

2.18 

1.01 

1.18 

1.96 

1.63 

.30 

.07 

1.42 

Cd 

^     22 

.97 

5.33 

3.06 

2.57 

2.08 

1.11 

1.29 

1.87 

1.55 

.24 

1.02 

1.56 

23 

1.06 

5.10 

2.9.3 

2.46 

.99 

1.22 

1.41 

1.79 

1.49 

.18 

.97 

1.70 

24 

1.16 

4.88 

2.80 

2.36 

91 

1.34 

1.54'     1.72 

1.42 

.13 

.93 

1.85 

25 

1.26 

4.69 

2.69 

2.26 

.83 

1.45 

1.67 

1.65 

1.37 

.09 

.90 

2.01 

26 

1  36 

4.51 

2.59 

2.18 

.76 

1.571 

1.81 

1.58 

1.32 

1.05 

.86 

2.18 

27 

1.46 

4.34 

2.49 

2.10 

.701.69 

1.95 

1.53!     1.27 

1  01 

.83 

2  36 

28 

1.57 

4.19 

2.40 

2  02 

.641.82 

2.10 

1.47 

1.22        .97 

.80 

2  54 

29 

1.68 

4.04 

2.32 

1.95 

.58 

1.95 

2.25 

1.42 

1.18 

.94 

2.73 

1 

52  WROUGHT  IRON  AND  STEEL. 

IRON  FLOOR  BEAMS. 

When  I  beams  are  used  as  floor  joists  or  girders,  the  spacing 
and  proper  size  of  beams  depends  on  the  amount  and  character 
of  the  loads,  as  well  as  the  distance  to  be  spanned.  Not  only  the 
positive  strength,  but  the  elasticity  or  amount  of  deflection  per- 
missible must  be  considered. 

A  heavy  load  per  unit  of  area  may  not  require  as  strong  a 
floor  as  that  necessary  for  a  lighter  one,  if  the  latter  be  liable  to 
sudden  application,  especially  if  accompanied  with  impact, 
while  the  normal  state  of  the  heavier  load  is  quiescence,  or  slow 
and  even  change.  It  would  require  a  special  treatise  to  describe 
the  subject,  and  those  lacking  experience  are  referred  to  the 
published  literature  which  is  now  very  ample  and  complete.  It 
has  been  demonstrated  that  the  greatest  mass  of  men  that  can 
be  packed  on  any  floor  will  not  exceed  in  weight  80  Ibs.  per 
square  foot.  The  weight  of  the  iron  beams  will  depend  on  the 
span,  for  which  see  a  general  rule  farther  on.  If  brick  arches 
are  Inid  between  the  beams,  the  weight  of  a  4"  course  of  brick, 
including  the  concrete  filling,  will  be  about  50  Ibs.  per  square  foot. 

Within  the  limits  of  length  of  span  in  which  rolled  I  beams 
can  be  used,  it  may  be  assumed  that  a  floor  is  safe  to  sustain  the 
greatest  possible  load  of  men,  when  the  following  loading  does 
not  exhibit  a  greater  bending  stress  on  the  beam  than  that  de- 
noted in  the  tables,  under  the  head  of  "  Greatest  Safe  Load  Dis- 
tributed," pages  40-51. 

I  Beam  joists  with  wooden  floor      —  100  Ibs.  per  square  foot. 
Wooden  floor  and  plastered  ceilings  =110  "     "        "        " 
4"  brick  arches  and  concrete  filling  —  150  "     "        "        " 

These  figures  represent  the  total  weight  of  floor  itself  and  the 
imposed  load. 

When  the  floor  beams  are  subject  to  the  action  of  moving 
loads,  it  is  necessary  to  make  allowance  for  a  greater  nominal 
weight  than  actually  may  occur,  especially  if  the  span  is  long 
in  proportion  to  the  depth  of  the  beam.  If  the  beams  are  too 
light,  the  resulting  tremor  and  vibration  will  be  a  source  of  dis- 
comfort to  the  user,  if  not  of  weakness  to  the  structure.  The 
same  results  are  obtained  by  assuming  either  a  higher  nominal 
load  per  unit  of  area  than  actually  can  occur,  or  adopting  a 
higher  factor  of  safety,  than  given  in  our  tables,  for  the  actual 


WEIGHT  OF  IRON  IN  FLOOB  BEAMS.  53 

loads.  Floors  proportioned  as  follows  for  given  purposes  will  be 
found  satisfactory.  The  weight  of  the  material  may  be  included 
in  the  figures. 


CHARACTER   OP  FLOOR. 

LOAD  PER  SQ.  FT. 

Very  lightest  floors,  plank  covering    . 

100  Ibs 

Very  lightest  floors,  brick  arches  

150   " 

Light  warehouse  floors 

9QO  " 

Halls  of  audience  

200   " 

Warehouses  in  which  heavy  pieces  are  moved.  . 
Shop  floors  for  light  machinery  

250  " 
250   " 

Shop  floors  for  heavy  machinery. 

300  to  500  Ibs 

GENERAL  RULE  FOR   THE  WEIGHT  OF  IRON  IN 
FLOOR  BEAMS. 

When  the  standard  section  of  any  size  of  beam  is  used, 
the  weight  of  iron  obtained  by  the  following  rule  will  be 
found  to  approximate  closely  to  the  actual  amount  required: 
"  Square  of  span  in  feet  divided  by  5  times  the  depth  of  the  beam 
in  inches,  equals  the  pounds  of  iron  in  the  beams  per  square 

foot  of  floor  "f-8^2,-,   =  Ibs 
\5  x  depth 

This  is  for  a  load  of  150  Ibs.  per  square  foot,  and  the  beams 
strained  up  to  the  maximum  safe  limit  as  given  in  the  tables. 

With  the  same  space  the  weight  of  the  beams  will  vary  directly 
as  the  load  varies,  consequently  the  weight  of  iron  for  any  other 
required  loading  per  square  foot  can  be  obtained  by  proportion 
from  above  rule.  Example. — A  floor  of  20  feet  span  is  subject 
to  a  load  of  150  Ibs.  per  square  foot.  The  weight  of  the  iron 

20 2 
beams  will  be  F~^TK  =5.33  Ibs.  per  square  foot  of  floor,  if  15" 

2Q2 

Beams  are  used,  or  if  12"  Beams  are  used  = ^  =  6.66  Ibs.  per 

square  foot.  To  these  figures  add  the  weight  of  ends  built  into 
the  wall,  which  should  be  from  6"  to  12"  at  each  end,  according 
to  the  span,  etc.  If  the  load  to  be  sustained  is  250  Ibs.  per  sq. 
foot,  on  15"  I  beams  the  necessary  weight  becomes  as  150  :  250  :: 
5.33  Ibs. :  8.88  Ibs.  per  square  foot. 


64  WKOUGHT  IKON  AND   STEEL. 

This  rule  applies  only  to  the  minimum  section  of  any  I  beam. 
If  the  section  is  increased,  the  weight  of  iron  required  will  also 
increase.  By  the  above  it  will  be  observed  that  the  deeper  the 
beam  used  the  less  the  amount  of  iron  required,  and  such  is  the 
case  as  a  general  rule.  But  for  short  spans  the  use  of  the  deep- 
est beams  might  require  too  wide  a  spacing  to  suit  the  covering 
of  the  floor.  Then  the  best  economy  requires  the  adoption  of  a 
shallower  and  lighter  beam.  For  brick  arches  for  fire-proof 
floors  it  is  usual  to  limit  the  rise  or  spring  from  3  to  6  inches,  in 
order  to  build  in  and  conceal  the  tie  rods,  which  should  not  be 
much  if  any  above  the  center  of  the  beam.  For  such  flat  arches 
the  spacing  of  the  beams  should  not  exceed  6  feet,  and  if  a 
single  4"  course  of  brick  is  used,  it  is  safest  not  to  exceed  5  feet 
separation.  Of  course  for  arches  of  more  rise  and  for  other 
special  purposes  than  indicated  above,  no  such  limitation  is 
necessary. 

SPACING  OF  FLOOR  BEAMS. 

The  following  rule  gives  the  greatest  distance  apart  that  floor- 
beams  can  be  placed  to  support  safely  any  given  load  per  square 
foot.  Multiply  the  length  of  span  in  feet  by  the  load  in  Ibs.  per 
square  foot.  Find  iu  the  table,  page  40,  the  safe  load  in  Ibs.  for 
a  beam  of  the  size  and  length  desirable  to  use.  Divide  this  safe 
load  by  the  product  first  found,  and  the  quotient  is  the  greatest 
distance  in  feet  that  the  beams  ought  to  be  placed,  center  to 


center.     Or  Distance  =         -.     w  =  Ibs.  per  square  foot. 

L  =  length  of  span  in  feet. 

Example.  —  A  floor  of  20  feet  span  with  its  full  load  will  weigh 
150  Ibs.  per  square  foot.  Different  sizes  of  beams  may  be  safely 
spaced  as  far  apart  as  follows  :  For  15"  —  145  Ib.  I  Beams 

80x150  =  10'8  feet  center  to  center-     For  13"  12°  lb-  l  beams 


The  tables  on  pages  56-62  show  the  greatest  distance  apart, 
center  to  center,  that  beams  should  be  placed  for  a  loading  (in- 
cluding the  weight  of  the  floor  itself)  of  100,  150,  200,  or  250  Ibs. 
per  square  foot. 


SPACING   OF  FLOOR  BEAMS.  55 

The  deflections  of  the  beams  which  are  given  .in  the  tables 
will  be  uniform  for  beams  of  the  given  spans  so  long  as  the  spac- 
ing is  proportioned  according  to  the  table. 

In  the  case  of  plastered  ceilings  or  other  circumstances  where 
undue  deflection  might  be  injurious,  it  is  considered  good  prac- 
tice to  limit  the  deflection  to  about  T,-£(T  of  the  span.  When 
the  deflections  exceed  this  amount,  the  corresponding  loads  in 
the  table  are  printed  in  small  figures.  When  the  deflection  is 
below  this  amount,  the  figures  for  the  loads  are  in  larger  print. 
The  proper  spacing  of  beams  for  any  load  is  inversely  propor- 
tioned to  the  loads.  Consequently  the  proper  distance  apart  for 
beams  for  any  load  per  square  foot  can  be  easily  obtained  di- 
rectly from  the  table  as  well  as  by  the  rule  previously  given. 

Rule. — Multiply  the  distance  given  in  the  table  by  150  and 
divide  by  the  number  of  Ibs.  per  square  foot  required  to  be  sus- 
tained. The  quotient  will  be  the  greatest  distance  apart  for  the 
beams. 

Example. — What  is  the  greatest  distance  apart  8"  65  Ibs,  I 
beams  can  be  placed  to  support  safely  a  load  of  220  Ibs.  per 
square  foot,  the  beams  having  a  clear  span  of  18  feet  ?  By  the 

table  the  spacing  for  150  Ibs.  per  foot  is  3.3  feet  ~*n1^>  —  2.25 

£/w 

feet,  the  distance  required. 


[UNIVERSITY 


56 


WROUGHT  IRON  AND   STEEL. 


PENCOYD 


o 


DECK  BEAMS. 


Greatest  distance  between  floor  beams  so  that  the  bending  stress  on  the 
beam  will  not  exceed  its  maximum  safe  load. 


1 

£ 

| 

•  of 

LENGTH  OP  SPAN  IN  FEET. 

1 

fc 

if 

8| 

O"  -! 
*§* 

10 

12 

14 

16 

18 

20 

g 

o  g 

H  ni 

P*            ^ 

es 

gs 

i 

o 

ft  0 
•< 

DISTANCE  BETWEEN  CENTRES  OP 

o 

02 

1 

3 

BEAMS   IN    FEET. 

100 

17.6 

13.5 

10.7 

8.6 

150 

11.7 

9.0 

7.1 

5.8 

60 

12 

104 

200 

8.8 

6.7 

5.3 

4.3 

250 

7.0 

5.4 

4.3 

3.5 

Deflection 

in  Inches. 

i 

.28 

.34 

.44 

.54 

100 

19.3 

14.2 

10.9 

8.6 

7.0 

150 

12.9 

9.5 

7.2 

5.7 

4.6 

61 

11 

91 

20  » 

9.7 

7.1 

5.4 

4.3 

3.5 

250 

7.7 

5.7 

4.3 

3.4 

2.8 

Deflection 

in  Inches. 

.21 

.29 

.37 

.46 

.58 

100 

2-2.1 

15.3 

11.3 

8.6 

6.8 

5.5 

150 

14.7 

10.2 

7.5 

5.7 

4.5 

3.7 

62 

10 

80 

200 

11.0 

5.6 

4.3 

3.4 

2.8 

250 

8.8 

0J 

4.5 

3.4 

2.7 

2.2 

Deflection 

in  Inches. 

.16 

.23 

.32 

.41 

.52 

.64 

100 

17.6 

12.2 

9.0 

6.9 

5.4 

4-4 

150 

11.7 

8.1 

6.0 

4.6 

3.6 

2-9 

63 

9 

72 

200 

8.8 

6.1 

4.5 

3.4 

2.7 

2-2 

250 

7.0 

4.9 

3.6 

2.7 

2.2 

1  •» 

Deflection 

in  Inches. 

.18 

.26 

.35 

.46 

.58 

•71 

100 

13.4 

9.3 

6.9 

5.2 

4-1 

3-4 

150 

9.0 

6.2 

4.6 

3.5 

2-8 

2-2 

64 

8 

61 

200 

6.7 

4.7 

3.4 

2.6 

2-  1 

1  -7 

250 

5.4 

3.7 

2.7 

2.1 

1  -7 

1  -3 

Deflection 

in  Inches. 



.20 

.29 

.b9 

.51 

•B5 

•to 

100 

9.2 

6.4 

4.7 

3- 

2-8 

2    3 

150 

6.1 

4.2 

3.1 

2- 

1  -9 

1  -5 

65 

7 

52 

200 

4.6 

3.2 

2.3 

1  • 

1  -4 

J-l 

250 

3.7 

2.5 

1.9 

1- 

1-1 

'• 

Deflection 

in  Inches. 

.23 

.33 

.45 

•& 

•75 

•92 

100 

6.8 

4.7 

3- 

2- 

2-1 

1  -7 

150 

4.5 

3.2 

2- 

I- 

1-1 

1  •  1 

66 

6 

42 

200 

3.4 

2.4 

1- 

1- 

1-1 

•9 

250 

2.7 

1.9 

1  • 

1  • 

•8 

•  7 

Deflection 

in  Inches. 

.27 

.39 

•f> 

-  6 

•87 

1  -07 

100 

4.5 

3-1 

2- 

]• 

150 

3.0 

2-1 

I- 

1  • 

67 

5 

34 

200 

2.2 

1  •« 

1- 

250 

1.8 

1-2 

Deflection 

in  Inches. 

.32 

•46 

•  6 

•  8 

FLOOR  BEAMS. 


57 


PENCOYD 


:Q  DECK 


BEAMS. 


Figures  in  small  type  denote  that  the  beams  so  placed  will  deflect  more 
than  J;-  of  an  inch  for  each  foot  of  span. 


LENGTH  OF  SPAN  IN  FEET. 

B 

O 

j. 

I 

£8^. 

H 

ft 

B| 

fe  g 

H 

H 

22 

24 

26 

28 

30 

32 

^h^ 

E--1 

a 

«* 

g 

DISTANCE  BETWEEN  CENTRES  OF 

^  ° 

o 

~  M 

s 

BEAMS   IN   FEET. 

o 

m 

7.1 

6.0 

5- 

4-4 

3-8 

3-4 

100 

4.8 

4.0 

3- 

2-9 

2- 

2-2 

150 

3.6 

3.0 

2- 

2-2 

1  • 

1  -7 

200 

104 

12 

60 

2.9 

2.4 

2- 

]  -8 

1  • 

1-3 

250 

.65 

.78 

•9 

1-00 

1-2 

1-33 

Deflection 

in  Inches. 

5.8 

4  -8 

4- 

3-6 

3- 

2-7 

100 

3.8 
o  ft 

3-2 

2- 

2-4 

2- 

1    8 

150 

el 

u.y 
2.3 

1  -9 

1-6 

1-4 

1- 

1-1 

200 
250 

91 

11 

ol 

.71 

•84 

•99 

1-15 

1  '  3 

1-50 

Deflection 

in  Inches. 

3-0 

2-6 

2-2 

]•» 

j. 

100 
150 

2-3 

1-9 

1  •  I) 

1  -4 

1- 

2ori 

80 

10 

62 

1  -8 

1  -5 

1-3 

1  •  1 

1  • 

250 

•78 

•93 

1-09 

1-26 

1  -4 



Deflection 

in  Inches. 

3-6 

3-1 

2-6 

2-2 

100 

2-4 

2-0 

1-7 

1-5 

150 

1  •  ti 

1-5 

1  -3 

1  •  1 

200 

72 

9 

63 

J-5 

1-2 

1  -0 

•9 

250 

* 

•66 

1-03 

1-21 

1-40 

Deflection 

in  Inches. 

2-8 

2-3 

2-0 

100 

1  -9 

1-R 

1-3 

150 

1-4 

1-2 

1  -0 

200 

61 

8 

64 

1-1 

•9 

•8 

250 

•97 

1-16 

1-36 

Deflection 

in  Inches. 

1-9 

100 

1-3 

150 

•9 

200 

52 

7 

65 

•8 

250 

I'lO 

Deflection 

in  Inches. 

100 

150 

200 

42 

6 

66 

250 

Deflection 

in  Inches. 

100 

150 

200 

34 

5 

67 

250 

Deflection 

in  Inches. 

58 


WROUGHT  IRON   AND   STEEL. 


PENCOYD 


BEAMS. 


Greatest  distances  between  centres  of  floor  beams,  so  that  the  bending 
stress  on  the  beam  will  not  exceed  its  maximum  safe  load. 


CHART  NUMBER. 

g 

Sis 

W  pq 

&1 

H  M 
• 

OD 

WEIGHT  PER  YARD, 

LBS. 

LOAD  PER  SQ.  FT. 
OF  FLOOR, 

LBS. 

LENGTH  OF  SPAN  IN  FEET. 

10 

12 

14 

16 

18 

20 

DISTANCE  BETWEEN  CENTRES  OF 
BEAMS  IN  FEET. 

1 
2 
3 

4 

• 

5 
t% 

6 

15 
Deflection 

15 
Deflection 

12 
Deflection 

12 
Deflection 

10* 
Deflection 

201 

Deflection 

1C* 
Deflection 

200 
in  Inches. 

145 
in  Inches. 

168 
in  Inches. 

120 
in  Inches. 

134 
in  Inches. 

108 
in  Inches. 

89 
in  Inches 

100 
150 
200 
250 

33.1 
22.1 
16.6 
13.3 
.27 

25.3 
16.9 
12.7 
10.1 
.27 

22.6 
15.1 
11.5 
9.0 
.34 

16.6 
11.1 
8.3 
<i.6 
.34 

16.8 
11.2 
8.4 
6.7 
.39 

13.6 
9.1 
6.8 
5.4 
.39 

11.3 
7.5 
5.6 
4.5 
.39 

26.2 
17.5 
13.1 
10.5 
.34 

20.0 
13.3 
10.0 
8.0 
.34 

17.9 
11.9 
8.9 
7.1 
.43 

13.1 
8.7 
6.5 
5.  '2 
.43 

13.3 
8.9 
6.6 
5.3 
.49 

10.7 
7.1 
5.4 
4.3 
.49 

8.9 
5.9 
4.4 
3.5 
.49 

21.2 
14.1 
10.6 
8.5 
.42 

16.2 
10.8 
8.1 
6.5 
.42 

14.5 
9.6 
7.2 
5.8 
.53 

10.6 
7.1 
5.3 
4.2 
.53 

10.7 
7.1 
5.4 
4.3 
.61 

8.7 
5.8 
4.3 
3.4 
.61 

7.2 
4.8 
3.6 
2.9 
.61 

100 
150 
200 
250 

100 
150 
200 
250 

29.5 
19.7 
14.8 
11.8 
.26 

21.7 

14!4 
10.8 
8.7 
.26 

2J.9 
14.6 
11.0 
8.8 
.30 

17.7 
11.8 
8.9 
7.1 
.30 

14.7 
9.8 
7.4 
5.9 
.30 

100 
150 
200 
250 

100 
150 

200 
250 

29.8 
19.9 
14.9 
11.9 
.22 

24.1 
16.1 
12.1 
9.7 
.22 

20.0 
13.3 
10.0 
8.0 
.22 

100 
130 
200 
250 

100 
150 
200 
250 

FLOOK  BEAMS. 


PENCOYD 


BEAMS. 


Figures  in  small  type  denote  that  the  beams  so  placed  will  deflect  more 
than  :j\r  of  an  inch  for  each  foot  of  span. 


LENGTH  OF  SPAN  IN  FEET. 

LOAD  PER  SQ.  FT. 
OF  FLOOR, 
LBS. 

WEIGHT  PER  YARD, 
LBS. 

M 
•<  . 

«! 

63 

$5 

O2 

CHART  NUMBER. 

22 

24 

26 

28 

30 

32 

DISTANCE  BETWEEN   CENTRES  OF 
BEAMS  IN   FEKT. 

17.5 
11.7 
8.8 
7.0 
.51 

13.4 
8.9 
6.7 
5.4 
.51 

12.0 
8.0 
6.0 
4.8 
.64 

8.8 
5.8 
4.4 
3.5 
.64 

14.7 
9.8 
7.4 
5.9 
.61 

11.3 
7.5 
5.6 
4.5 
.61 

10.0 
6.7 
5.0 
4.0 
.77 

7.4 

4.9 

12.5 
8.4 
6.3 
5.0 
.11 

9.6 
6.4 
4.8 
3.9 
.72 

8-» 
5-7 
4-3 
3-4 

•90 

«-3 
4-2 

10.8 
7.2 
5.4 
4.3 
.83 

8.3 
5.5 
4.1 
3.4 
.83 

7-4 
4-9 
3-7 
3-0 
1  -05 

5-4 
3-6 

9.4 
6.3 
4.7 
3.8 
.95 

7.2 

4.8 
3.6 
2.9 
.95 

B- 
4- 

2- 
1  -2 

4-7 

8- 
5- 
4  • 

3. 

1  -0 

6- 
4  • 

2- 
1  -0 

5- 
3- 
2- 
»• 

1-3 

4- 
2- 

100 
150 
2CO 
250 

100 
150 
200 
250 

200 
Deflection 

145 
Deflection 

168 
Deflection 

120 
Deflection 

134 
Reflection 

108 
Reflection 

89 
Deflection 

15 

in  Inches 

15 
in  Inches 

12 
in  Inches 

12 
in  Inches. 

1C1 
in  Inches. 

ICi 
in  Inches. 

1C* 
n  Inches. 

1 
2 
3 
4 
5 

ei 

6 

100 
150 
200 
250 

100 
150 
2(0 
250 

2.9 
.77 

2-5 
•30 

2-2 
1-05 

1  -9 
1-20 

1-36 

4-a 

100 

4.4 

3-5 
•74 

7-2 
4-8 
3-6 
2-9 

3-7 
3-0 

•88 

3-2 
2-6 
1'03 

2-7 
2-3 
1-19 

2-4 
1  -9 
1-37 

2- 
1  •  5 

150 
200 
250 

100 
150 
200 
250 

100 
150 
200 
250 

4*0 

3-0 
2-4 

3-4 
2-6 
2-1 

2-9 
2-2 

1  -8 

2-6 
1  -9 
1-5 

2- 
1- 

1- 

1  • 
1'57 

2-4 
•74 

2-0 

•88 

1-7 

1-03 

1  '4 
1-19 

1  '3 
1-37 

60 


WEOUGHT   IKON    AND    STEEL. 


PENCOYD 


BEAMS. 


Greatest  distances  between  centres  of  floor  beams,  so  that  the  bending 
stress  on  the  beam  will  nut  exceed  its  maximum  safe  load. 


i 

g 
% 

1 

6 

LENGTH  OF  SPAN  IN  FEET. 

§ 

la 

|y 

*§„• 

10 

12 

14 

16 

18 

20 

j^ 

&  s 

SQ 

S  j  pfl 

S 

^ 

m1" 

fcSe,  ^ 

a 

s 

2 

<  O 

DISTANCE  BETWEEN  CENTRES  OF 

a 

£ 

S 

BEAMS  IN  FEET. 

100 

32.4 

29.5 

16.5 

12.7 

10.0 

8.1 

150 

21.6 

15.0 

11  0 

8.4 

6.7 

5.4 

7 

10 

112 

200 

16.2 

11.3 

8.3 

6.3 

5.0 

4.1 

Deflection 

in  Inches. 

250 

13.0 
.16 

9.0 
.23 

6.6 
.31 

5.1 
.41 

4.0 
.52 

3.2 
.C4 

100 

27.7 

19.2 

14.1 

10.8 

8.5 

6.9 

150 

18.4 

12.8 

9.4 

7.2 

5.7 

4.6 

8 

10 

90 

200 

13.8 

9.6 

7.1 

5.4 

4.3 

3.5 

250 

11.1 

7.7 

5.6 

4.3 

3.4 

2.8 

Deflection    in  Inches  . 

.16 

.23 

.31 

.41 

.52 

.64 

100 

24.6 

17.1 

12.6 

9.6 

7.6 

6-2 

150 

16.4 

11.4 

8.4 

6.4 

5.1 

4-1 

9 

9 

90 

200 

12.3 

8.6 

6.3 

4.8 

3.8 

3-1 

250 

9  '•' 

6.8 

5.0 

3  8 

3.0 

2  •  5 

Deflection 

in  Inches. 

.is 

.26 

.35 

.46 

.58 

•71 

100 

19.6 

13.6 

10.0 

7.7 

6.1 

4-9 

150 

13  1 

9.1 

6.7 

5.1 

4.0 

3-3 

10 

9 

70 

200 

9.8 

6.8 

5.0 

3.8 

3.0 

2-4 

250 

7.8 

5.4 

4.0 

3.1 

2.4 

2-0 

Deflection 

in  Inches. 

.18 

.26 

.35 

.46 

.58 

•71 

100 

19.6 

13.6 

10.0 

7.7 

6- 

4-9 

150 

13.1 

9.1 

6.7 

5.1 

4  • 

3-3 

11 

8 

81 

200 

9.8 

6.8 

5.0 

3.8 

S- 

2-4 

250 

7.8 

5.4 

4.0 

3.1 

2- 

2-0 

Deflection 

in  Inches. 

.20 

.29 

.39 

.51 

•6 

•80 

100 

16.1 

11.2 

8.2 

6.3 

5- 

4-0 

150 

10.7 

7.5 

5.5 

4.2 

3- 

2-7 

12 

8 

65 

200 

8.1 

5.6 

4.1 

3.2 

2- 

2-  0 

250 

6.5 

4.5 

3.3 

2.5 

2- 

1-6 

Deflection 

in  Inches. 

.20 

.29 

.39 

.51 

•6 

•80 

100 

13.3 

9.2 

6.8 

4- 

3-3 

150 

8.8 

6.1 

4.5 

2- 

2-2 

13 

7 

65 

200 

6.6 

4.6 

3.4 

2- 

1  -7 

250 

5.3 

3.7 

2.7 

1- 

1-3 

Deflection 

in  Inches. 

.23 

.33 

.44 

s 

•7 

•90 

100 

11.5 

8.0 

5.9 

3- 

2-9 

150 

7.7 

5.3 

3.9 

2- 

1  -9 

14 

7 

52 

200 

5.7 

4.0 

2.9 

I- 

1-4 

250 

4.6 

3.2 

2.3 

1- 

1-1 

Deflection 

in  Inches. 

.23 

.33 

.44 

•5 

•74 

•90 

1 

FLOOB  BEAMS. 


61 


PENCOYD 


BEAMS. 


Figures  in  small  type  denote  that  the  beams  so  placed  will  deflect  more 
thau  3\r  of  an  inch  for  each  foot  of  span. 


LENGTH  OP  SPAN  IN  FEET. 

Ki 

o>ef 

ati  O  • 

«38 

F 

WEIGHT  PER  YARD, 
LBS. 

£«£ 

n 

o| 

»z 

OB 

CHART  NUMBER. 

22 

24 

26 

28 

30 

32 

DISTANCE  BETWEEN   CENTRES   OF 
BEAMS  IN   FEKT. 

8-7 
4-5 

6-6 
3-7 

4-8 
3-2 

4-1 

2-8 

3- 
2- 
I- 

1- 
1*4 

100 
150 
200 
250 

112 
Deflection 

90 
Deflection 

90 
Deflection 

70 
Deflection 

81 
Deflection 

65 

Deflection 

65 
Deflection 

52 
Deflection 

10 
in  Inches. 

10 
in  Inches. 

9 

in  Inches. 

9 
in  Inches. 

8 
in  Inches. 

8 
in  Inches. 

7 
in  Inches. 

7 
in  Inches. 

7 
8 
9 
10 
11 
12 
13 
14 

2-7 
•78 

2-3 

•92 

1  -9 
1-06 

1-1 

1-26 

100 
150 
200 
250 

8-8 
2-9 

2-4 

2-0 

1-8 

1- 

•78 

•92 

l-O.'j 

1'2« 

1*44 

100 
150 
200 
250 

3-4 
2-5 
2-0 

•86 

4-0 
3-7 
2-0 
1  -6 

•86 

4-0 
2-7 
2-0 
1-6 

•97 

3-3 
2-2 
1  -7 
1-3 

•97 

2-7 
1-4 
1-09 

2-4 
1-6 
1-2 
•9 
1-09 

2-8 
2-1 
1-7 
1-02 

3-4 
2-3 
1-7 
1-4 
1-02 

3-4 
2-3 
1-7 
1-4 
1-16 

2-8 
1-9 
1-4 

1-18 

2-3 
1  •  5 
1-2 
•9 
1-32 

2-0 
1  -3 
1-0 
•8 
1-32 

2-4 

1-8 
1-5 
1-21 

2-9 
2-0 
1-4 
1-2 
1-21 

2-9 
1  -9 
1-4 
1-2 
1-36 

2-4 
!•  6 
1-2 
1  -0 
1-36 

2-1 
1-8 
1-3 
1-40 

2-5 
1-7 
1*9 

1-0 
1-40 

100 
150 
200 
250 

100 
150 
200 
250 

100 
150 
2UO 
250 

100 
150 
200 
250 

100 
150 
200 
250 

WEOUGHT   IRON  AND   STEEL. 


PENCOYD 


BEAMS. 


Greatest  distance  between  centres  of  floor  beams  so  that  the  bending 
stress  on  beam  will  not  exceed  its  maximum  safe  load. 

Figures  in  small  type  denote  that  the  beams  so  placed  will  deflect  more 
than  ^  of  an  inch  for  each  foot  of  span. 


t 

m 
p 
fc 

15 
16 
17 
18 
19 
20 
21 
22 

SIZE  or  BEAM 

IN  INCHES. 

WEIGHT  PER  YARD, 

LBS. 

£  : 
f 

LENGTH  OP  SPAN  IN  FEET. 

10 

12 

14 

16 

18 

20 

DISTANCE  FETWEEN  CENTRES  OP 

BEAMS   IN   FEET. 

6 

Deflection 

6 
Deflection 

5 

Deflection 

5 
Deflection 

4 

Deflection 

4 
Deflection 

3 

Deflection 

3 
Deflection 

50 
in  Inches. 

40 
in  Inches. 

in  Inches. 

30 
in  Inches. 

28 
in  Inches  . 

18.5 
in  Inches. 

23 
in  Inches. 

17 
in  Inches  . 

100 
150 
200 
250 

8.4 

5.6 
4.2 
3.3 
.27 

7.5 
5.0 
3.7 
3.0 
.27 

E.O 
3.3 
2.5 
2.0 
.32 

4.7 
3.1 
2.3 
1.9 
.32 

R.8 
3.9 
2.9 
2.3 
.38 

5.2 
3.5 
2.6 
21 
.38 

2-8 
2-  1 
1  -7 
•62 

3-8 
2-6 
1  -9 
1-5 
•52 

2-2 
1-6 
1-3 

2-9 
1-9 
1-5 
1-2 
•69 

1-7 
1-3 
1-0 

•H7 

2-3 
1-5 
1  -2 
•9 
•67 

1-4 
1  -0 
•8 
1  -07 

1-9 
1-2 
•9 
•  7 
1-07 

100 

rso 

200 
250 

100 
150 
200 
250 

100 
150 
201) 
250 

2-3 

1-7 

1  •  3 

1-0 

•9 

1-4 

•46 

3-2 
2-  1 

J  -0 
•63 

2-4 
1  -6 

•8 
•82 

1  -8 
1-2 

•8 
1-04 

1-4 
•9 

•5 
1-29 

1-2 

•8 

1-3 

•46 

1  -0 

•63 

•7 
•82 

•6 
1  -04 

•5 

1-29 

100 
150 
200 
250 

100 
150 
200 
250 

100 
150 
200 
250 

100 
150 

200 
250 

2-4 
1  -8 
1-4 

1-7 
1-2 
1-0 

1-2 

•9 

•9 
•7 
•6 

•7 
•6 
•4 

2-4 

1  -6 

1-7 

1-2 

•8 

•« 

•7 
•6 

1-0 

•40 

2-0 
1  -3 
1-0 
•8 
•63 

1-8 
1  •  1 

•8 

•63 

1-4 

•  7 
•6 

•77 

.7 

•  a 

•  4 

•  77 

•  5 
•79 

1-0 
•7 
•5 
•  4 
1-05 

0-8 
•5 
•4 
•3 
1  -05 

•4 

1  -03 

•8 
•5 
•  4 
•3 

1-37 

•8 
•4 
•3 
•2 
1-37 

•3 

1-31 

LATERAL  STRENGTH  OF  FLOOR  BEAMS.  63 

TIE  RODS  FOR  BEAMS  SUPPORTING  BRICK  ARCHES. 
The  horizontal  thrust  of  Brick  arches  is  found  as  follows  : 

1.5  Wl? 

—  ^  —  =  pressure  in  Ibs.  per  lineal  foot  of  arch. 

W  =  Load  in  Ibs.  per  square  foot. 

L  —  Span  of  arch  in  feet 

R  =  Rise  in  inches. 

Place  the  tie  rods  as  low  through  the  webs  of  the  beams  as 
possible,  and  spaced  so  that  the  pressure  of  arches  as  obtained 
above  will  not  produce  a  greater  stress  than  15,000  Ibs.  per 
square  inch  of  the  least  section  of  the  bolt. 

Example.  —  The  beams  supporting  an  arched  brick  floor  are 
five  feet  apart,  and  the  rise  of  the  arches  is  six  inches.  The  to- 
tal weight  of  floor  and  load  equals  150  Ibs.  per  square  foot. 

-^?-—  =  937.5  Ibs.   pressure  per  lineal  foot  of 


arch.  If  one-inch  screw  bolts  are  used  which  have  an  effective 
section  of  -ft-  square  inches.  Then  .6  x  15,000  =  9,000  Ibs.  which 
is  the  greatest  load  the  bolt  should  be  allowed  to  sustain,  and 

9  000 

-^r—  —  =  9.6  feet  =  greatest  distance  apart  of  the  bolts,  or  in 

9o7.5 

same  manner  we  would  find  5.3  feet,  if  «  inch  tie  rods  are  used. 

Ordinarily  it  wiJl  be  found  necessary  to  limit  the  spacing  of 
the  tie  rods  to  avoid  excessive  bending  stress  on  the  outer  beams 
of  the  floor,  or  to  prevent  this  bending  stress  being  transferred  to 
the  walls  of  the  building. 

The  ability  of  the  outer  beams  to  resist  the  horizontal  bending 
action  caused  by  the  pressure  of  the  arches  is  determined  as  fol- 
lows : 

LATERAL  STRENGTH  OF  FLOOR  BEAMS. 
The  resistance  to  bending  of  any  I  Beam  or  Channel  bar,  for 
a  force  acting  at  right  angles  to  the  web,  or  in  the  direction  of 
the  flanges, 

w  =         for  I  Beams- 


ft  T 

W  =  f-T,,  for  Channels. 


64:  WROUGHT  IRON  AND  STEEL. 

W  =  Safe  distributed  load  in  net  tons. 
L  =  Length  in  feet  between  supports. 
F  —  Width  of  flange  in  inches. 

/  =  Moment  of  inertia,  axis  coincident  with  web,  see  col. 
viii.,  pages  92-101. 

The  above  gives  results  which  have  been  proved  by  experiment 
not  to  exceed  one-third  the  ultimate  strength  of  the  beams.  The 
formulae  given  properly  apply  to  beams  secured  at  each  end 
only.  If  the  beam  is  of  considerable  length  requiring  supports 
at  several  points,  it  can  be  considered  as  continuous  (see  page 
75),  and  the  formulae  become, 

W  =       ,  for  I  Beams. 


127 

W  =         for  Channels. 


Example.— K  9-inch  70  Ib.  I  Beam  forming  the  outer  support 
for  an  arched  brick  floor  has  the  tie  rods  at  intervals  of  6  feet. 
What  evenly  distributed  horizontal  pressure  will  it  safely  resist  ? 
/=5.6  (see  col.  viii.,  page  92).  F=4^  inches  (see  col.  C, 

page  2).     Then  W=  15Q  *  ^_6-  =  3.4  tons  or  1,130  Ibs.  per  lin- 
eal foot  of  arch. 
Knowing  the  amount  of  the  load  W  and  requiring  the  distance 

L,     Above  equation  becomes  L?  —  -==7-=  in  which  W1  =  pres- 

W  Jf 

sure  or  load  on  beam  per  lineal  foot. 

.Example. — An  8"  43  Ib.  channel  bar  forms  the  end  support 
for  a  system  of  brick  arches  having  a  span  of  4  feet  and  4  inches 
rise.  How  closely  ought  tie  rods  to  be  placed  so  that  the  chan- 
nels will  not  be  overstrained  ?  The  horizontal  thrust  per  lineal 

foot  of  arch  =  1'5  x  ^°  x  16  =  900  Ibs.  or  .45  tons.     I  -  2.17. 

F=W*. 

12  x  2.17 


BEAMS   SUPPORTING  BRICK  WALLS. 


65 


It  will  generally  be  found  that  an  angle  bar  makes  a  better 
and  more  economical  support  for  the  arches  on  the  side  walls 
than  either  an  I  beam  or  channel. 

The  resistance  to  bending  of  an  angle  is  readily  found  by  the 
rule  given  on  page  69. 

W  =  - — - —  =  safe  distributed  load  for  a  non-continuous 
Li 

beam. 

1  4A.D 

W  —  -4-= —  =  safe  distributed  load  for  a  continuous  beam. 
Li 


And  as  before  Lz  = 


1AAD 


A  being  the  sectional  area  in 


square  inches,  and  D  the  width  or  size  of  the  angle  in  inches. 

Applying  this  rule  to  the  last  example,  and  considering  the  8" 
channel  replaced  by  a  4"  x  4'  x  i"  angle  whose  area  =  3. 75 
square  inches. 

1.4  x  3.75  x  4 


.45 


=  46 . 6  or  L  =  6 . 8  feet  between  centers 


of  boits.     Stress  on  bolts  900  x  6.8  =  6,120  Ibs.     To  resist  this 
|"  would  be  the  proper  diameter  of  the  screw. 


BEAMS  SUPPORTING  BRICK  WALLS. 

If  the  wall  has  no  openings  and  the  bricks  are  laid  with  the 
usual  bond,  the  prism  of  wall  that  the  beam  sustains  will  be  of 


66  WBOUGHT  IRON  AND  STEEL. 

a  triangular  shape,  the  height  being  one-fourth  of  the  span. 
Owing  to  frequent  irregularities  in  the  bonding,  it  is  best  to  con= 
sider  the  height  as  one-third  of  the  span. 

The  weight  of  brick  work  for  each  inch  of  thickness,  is  about 
10  Ibs.  per  square  foot.  Therefore  the  weight  of  the  triangular 
mass  of  brick  that  the  beam  supports  is  found  as  follows  : 

span, 

x  — o~~  in  feet 
x  10  times  the  thickness  of  the  wall  in  inches 


=  weight  in  Ibs.  ;  or  reducing  above  to  its  more  concise  form, 


W  =  Weight  in  Ibs.  supported  by  the  beam. 
t  —  Thickness  of  wall  in  inches. 
s  —  Span  of  beam  in  feet. 

The  greatest  bending  stress  at  the  center  of  the  beam,  result- 
ing from  a  brick  wall  of  above  shape,  is  the  same  as  that  caused 
by  a  load  one-sixth  less  concentrated  at  the  center  of  the  beam. 

Example.  —  What  beam  will  be  required  to  span  an  opening  of 
16  feet,  and  carry  a  solid  brick  wall  8  inches  thick,  the  beam  not 
to  be  strained  more  than  one-third  of  its  ultimate  strength  ? 

Weight  of  wall  by  the  rule.  W  =  1(    *  ^  256  rr  3,4  1  3  Ibs. 

Considering  the  load  as  in  middle  of  beam,  it  would  be  five- 
sixths  of  above  =  2,845  Ibs.,  or  5,690  Ibs.  if  evenly  distributed. 

By  our  table  page  43,  a  7"  I  beam  52  Ibs.  per  yard,  comes  near- 
est to  what  is  required,  its  greatest  safe  distributed  load  being 
3.5  tons.  The  deflection  under  this  load  will  be  about  .45  of  an 
inch,  found  as  described  on  page  89. 

If  a  wall  has  openings  such  as  windows,  etc..  the  imposed 
weight  on  the  beam  may  be  greater  "than  if  the  wall  is  solid. 

For  such  a  case  consider  the  outline  of  the  brick,  which  the 
beam  sustains,  to  pass  from  the  points  of  support  diagonally  to 
the  outside  corners  of  the  nearest  openings,  then  vertically  up 
the  outer  line  of  the  jambs,  and  so  on  if  other  openings  occur 
above.  If  there  should  be  no  other  openings,  consider  the  line 
of  imposed  brick  work  to  extend  diagonally  up  from  each  upper 
corner  of  the  jambs,  the  intersection  forming  a  triangle  whose 
height  is  one-third  of  its  base,  as  described  at  beginning. 


FORMULAE  FOB  ROLLED  IRON  BEAMS.  67 

APPROXIMATE  FORMULA  FOR  ROLLED  IRON 
BEAMS. 

The  following  rules  for  the  strength  and  stiffness  of  rolled 
iron  beams  of  various  sections  are  intended  for  convenient  ap- 
plication in  cases  where  strict  accuracy  is  not  required. 

The  rules  have  been  derived  from  the  authoritative  formula?. 
Those  for  rectangular  and  circular  sections  are  correct,  while 
those  for  the  flanged  sections  are  limited  in  their  application  to 
the  standard  shapes  as  given  in  our  tables.  They  will  be  found 
to  give  results  which  have  been  proved  by  experiment  to  be  suf- 
ficiently accurate  for  practical  purposes.  When  the  section  of 
any  beam  is  increased  above  the  standard  minimum  dimensions, 
the  flanges  remaining  unaltered,  and  the  web  alone  being  thick- 
ened, the  tendency  will  be  for  the  ultimate  load  as  found  by  the 
rules  to  be  in  excess  of  the  actual,  but  within  the  limits  that  it 
is  possible  to  vary  any  section  in  the  rolling,  the  rules  will  apply 
without  any  serious  inaccuracy. 

IN  THE   TABLES   OF   FORMULAE 

Column     I.  indicates  the  cross  section  of  the  beam. 

Column  II.  gives  the  ultimate  load  applied  at  the  center  of  a 
beam  supported  at  each  end. 

Column  III.  gives  the  ultimate  load  uniformly  distributed  over  a 
beam  supported  at  each  end. 

Column  IV.  indicates  the  deflection  under  any  load,  w  (not  ex- 
ceeding one-half  the  ultimate  load)  at  the  middle 
of  the  beam. 

Column  V.  gives  the  deflection  for  a  load  uniformly  distributed. 

SAFE  LOADS. 

The  ultimate  load  given  in  the  tables  is  defined  on  page  32. 
One- third  of  this  should  be  accepted  as  the  greatest  safe  station- 
ary load,  and  from  one-fourth  to  one-sixth  of  the  same  when  a 
moving  or  fluctuating  load  is  imposed,  according  to  the  way  it  is 
applied,  cr  the  degree  of  stiffness  required.  See  table,  page  34. 

10  A  =  WEIGHT   PER  YARD   IN   LBS. 

The  area,  A,  of  any  cross  section  of  wrought  iron  may  be  ob- 
tained by  dividing  its  weight  per  yard  by  10  ;  and  vice  versa,  its 
weight  per  yard  may  be  found  by  multiplying  its  area  in  square 
inches  by  10  ;  e.g.  the  area  of  a  beam  weighing  50  Ibs.  per  yard 
is  five  square  inches. 


68 


WEOUGHT  IBON  AND   STEEL. 


«* 


a 


•?.«! 


FORMULA   FOB  WROUGHT   IRON  BEAMS. 


€9 


s 


^ 

SJ 

^ 

-^ 

Q 

^ 

00    °° 

o*     °° 

CD        "^ 

(^                o       « 

H 

1-1    OJ 

W        CO 

w       "^ 

CO       ^ 

fc 


I 


5t= 


i 


|\  _  /I 

IT    "\| 


70  "WROUGHT  IEON  AND   STEEL. 

EXAMPLES  CALCULATED  FROM  PRECEDING  TABLES. 
SOLID  RECTANGULAR  SECTIONS. 

Example  1.  —  To  find  the  breaking  load  for  any  solid  rectan- 
gular beam  loaded  in  the  middle. 

~r        C  =  Solid  rectangular  bar,  2   inches  wide,  4  inches 
j*  deep  and  10  feet  between  supports.     Then,  from  For- 

1    mula  No.  1  ,  we  have  —  —  *      x     —4.16  tons    breaking 

lv 

load  in  middle  of  beam. 

Example  2.  —  To  find  the  uniformly-distributed  breaking  load 
for  same  beam. 

Formula  No.  2.  ?'6  x  8  —  =  8.32  tons  breaking  load  uni- 
formly distributed. 

Example  3.  —  To  find  the  deflections  for  above  beam  under  the 
greatest  safe  loads  ;  viz.,  one-third  breaking  loads. 


Formula  No.  3.  *'39  *  =0.36  inches,  for  a  load  of  1.39 

oO  x  8  x  lo 

tons  in  middle. 

Formula  No.  4.   -77  x  10?°  =  0.45  inches,  for  a  load  of  2.77 
48  x  8  x  16 

tons  distributed. 


HOLLOW  RECTANGULAR  SECTIONS. 

Example  4.—  To  find  the  breaking  loads  for  any  hollow  rec- 
tangular beam  supported  at  both  ends. 

Let  0  be  a  hollow  rectangular  section,  4  inches  wide, 
"t    8  inches  deep,  external  dimensions  ;  3  inches  wide,  6 
inches  deep,  internal  dimensions;  15  feet  between  sup- 
ports. 


Formula  No.  5.  ™_K*JL9-  <18  *  6U=  13.83tons,break- 
15 

ing  load  in  middle  ;  and  multiplying  this  result  by  2,  we  have 
25.66  tons  for  the  breaking  load  uniformly  distributed. 


EXAMPLES   FROM   PRECEDING   TABLES.  71 

Example  5.  To  find  the  deflection  of  this  beam  with  three  tons 
in  middle  ;  also  with  six  tons  distributed. 


flection  with  three  tons  in  middle. 
Formula  No.  8.  J-..,  inehes  de. 


flection  with  six  tons  distributed. 


SOLID  AND  HOLLOW  CYLINDERS. 

The  preceding  examples  for  rectangles  will 
apply  to  the  circular  sections  by  merely  sub- 
stituting the  proper  co-efficients  as  given  in 
Formulae  9  to  16  inclusive. 


EVEN-LEGGED  ANGLES  AND  TEES. 

Example  6.  —  To  find  the  breaking  loads  for  an  even-legged 
angle  or  tee,  used  as  a  beam  supported  at  both  ends. 

Weight,  37  Ibs.  per  yard  or  3.7  square 
't,  inches  section;  12  ft.  between  supports. 

Formula  No.  18.  2'S  * 


tons  breaking  load  uniformly  distributed,  or  1.73  tons  breaking 
load  in  the  middle. 

Example  7.—  To  find  the  deflection  of  the  above  beam  under 
a  load  suspended  from  the  middle  of  the  beam. 
Load  =  1500  Ibs.  =  .  75  tons. 


Formula  No.  19.     '  6  =  -64  inches  deflection- 

Theoretically  an  angle  has  the  same  transverse  strength  as  a 
tee  of  the  same  dimensions.  But  owing  to  the  difficulty  of  dis- 
posing the  load  as  symmetrically  on  the  angle  as  on  the  tee,  the 
latter  shape  generally  yields  better  results  by  experiment. 


72  WROUGHT  IRON  AND   STEEL. 

CHANNEL  BARS. 

Example  8. — To  find  the  breaking  loads  for  a  channel  bar 
used  as  a  beam  supported  at  both  ends. 

Channel  bar  9  inches  deep,  70  pounds  per  yard ;  7  square 
inches  section,  14  feet  between  supports. 

Formula  No.  22.  — --*^—  -  =  17.1  tons  distributed 

breaking  load,  or  half  this  weight  will  be  the  breaking  load  in 
the  middle. 

Example  9.  — To  find  the  deflection   of  above  beam  under 
greatest  safe  distributed  load. 
17.1 


3 


=  5.7  tons  greatest  safe  distributed  load. 


Formula  No.  24.   j>.7  x  2744  _  g  g  •    ^     deflection. 
80  x  7  x  81 


I  BEAMS. 

Example  10.  —  To  find  the  breaking  loads  for  an  I  'beam, 
loaded  in  the  middle  and  supported  at  both  ends. 

A  15"  I  beam,  200  Ibs.  per  yard,  20  square  inches  area, 

20  feet  between  supports.   Formula  No.  29.  2-1  x  20- 

=  31  .  5  tons  middle  breaking  load  ;  one-third  of  which 
(10.5  tons)  will  be  greatest  safe  load  in  middle,  or  twice 
this  (21  tons)  equals  greatest  safe  load  distributed. 

Example  11.—  To  find  the  deflections  for  the  same  I  beam 
under  the  above  greatest  safe  loads. 


Formula  No.  31.  =  .33  inches  under  a  load  of 

56  x  20  x  225 

10.5  tons  in  the  middle. 

Formula  No.  32.      21  *  800(L,g  =  .41  inches  under  a  load  of 
90  x  20  x  225 

21  tons  uniformly  distributed. 

Although  the  preceding  rules  for  I  beams  and  channels  give 
results  which  are  substantially  correct  for  all  the  standard  sec- 


EXAMPLES  FROM  PRECEDING  TABLES.  73 

tions  as  ordinarily  rolled,  yet  they  are  not  strictly  accurate,  and 
not  applicable  to  the  heavier-built  beams,  whose  flanges  are 
much  larger,  relatively  to  the  web,  than  is  the  case  in  the  aver- 
age rolled  beams.  For  such  cases,  the  following  formula  is 

,      Q.QA'D'  +  l.2a'df     ,       ,  .      ,     ,  . 
correct.     = — breaking  load  in  middle  of  beam. 

A'  =  Area  of  one  flange. 

D  =  Depth  between  centres  of  flanges. 

a  =  Area  of  web. 

d  =  Depth  of  web. 

For  example,  a  beam  20  inches  deep,  flanges  8"  x  1",  web  £" 
- ,  thick,  20  feet  between  supports, 

6.6  x  8  x  19"  +  1.2  x  4.5  x  18 

— —  55  tons 
20 

breaking  load  in  middle  of  beam ;  whereas  the  Rule  in 
Table  for  Rolled  Beams  would  give  a  similarly  placed  load  of 
2.1  x  20.5  x  20 


20 


=  43  tons. 


When  the  load  is  concentrated  away  from  the  centre  of  beam, 
the  ultimate  load  will  be  to  the  load  at  centre  as  the  square  of 
half  the  span  is  to  the  product  of  the  segments  formed  by  posi- 
tion of  load. 

Example. — A  beam  20  feet  between  supports  has  its  load 
placed  5  and  15  feet  respectively  from  each  end  :  the  breaking 
load  at  that  point  is  to  the  calculated  breaking  centre  load  as  100 
is  to  75. 

BEAMS  HAVING  NO  LATERAL  SUPPORT  BETWEEN 
BEARINGS. 

If  beams  are  us?d  without  any  support  sideways,  the  ten- 
dency to  fail,  by  lateral  bending  of  the  top  flange,  will  increase 
with  the  length  of  the  beam ;  and,  in  such  cases,  it  is  better  to 
limit  the  application  of  the  preceding  rules  to  beams  whose 
lengths  do  not  exceed  20  times  the  width  of  the  flange,  gradually 
increasing  the  factor  of  safety  for  longer  beams  ;  so  that,  when 


74  WROUGHT  IRON  AND   STEEL. 

the  beam  reaches  a  length  equal  to  70  times  the  width  of  the 
flange,  the  greatest  safe  load  would  be  about  one-sixth  of  the 
calculated  breaking  load,  or  the  proper  factor  of  safety  for  the 
latter  beam  would  be  double  that  for  the  former.  (See  page  36.) 

CANTILEVER  BEAMS. 

The  application  of  the  preceding  rules  to  overhanging  beams 
fixed  at  one  end  and  free  at  the  other,  is  best  indicated  by  sup- 
posing a  beam  with  both  ends  supported  to  be  inverted,  and  the 
reaction  of  the  supports  considered  as  the  positive  load. 

w  w 

/ 


It  is  then  evident  that  a  beam,  A  C  (see  above  illustration), 
both  ends  supported,  will  be  strained  with  a  middle  load,  W,  in 
an  equal  manner  to  a  cantilever,  A  B  or  B  C,  of  half  the  length 
of  A  G  and  having  a  similar  section,  and  bearing  one-half  the 


load(orf) 


at  its  end. 


EXAMPLES    FOR   CANTILEVER   BEAMS. 

A  rectangular  bar,  6"  x  2",  built  into  a  wall  and  projecting 
eight  feet.  For  load  concentrated  at  its  end,  take  one- 
fourth  the  co-efficient  in  Table  for  Beams  with  both  ends 

supported  and  load  in  middle.  —  =2.9  tons 

ultimate  load.    Deflection  under  one-third  of  above,  or  say  nine- 
tenths  of  a  ton ;  substituting  one-sixteenth  of  the  co-efficient  for 

9  x  512 
deflection  when  load  is  in  middle.    — ~  =  0.56  inches 

deflection  at  end. 

A  12-inch  I  beam,  15  square  inches  section,  extends 
10  feet  beyond  a  rigid  support.  For  a  load  evenly  dis- 
tributed, take  one-fourth  the  co-efficient  for  a  beam 
supported  at  both  ends,  bearing  a  distributed  load. 

1.05  x  15  x  12      ->y  *  .1        u      i  •      i     j  j-  x  M    j.   i 
-^ =  18 . 9  tons  breaking  load  distributed. 


EXAMPLES  FKOM  PBECEDING  TABLES.  75 

For  deflection  under  five  tons  distributed,  substitute  one-sixth 
of  the  co-efficient  for  deflection  in  Rule  for  Beams  supported  at 

both  ends  with  load  in* middle.  — -^  =  0.25 inches 

deflection  at  end  of  beam. 


CONTINUOUS  BEAMS. 

When  a  beam  is  continuous  over  several  supports,  or  when 
both  ends  are  as  rigidly  secured  as  is  necessary  at  the  fixed  ends 
of  a  cantilever,  the  beam  is  practically  in  the  same  condition  as 
a  non-continuous  beam  of  shorter  span. 

When  the  load  is  applied  at  the  middle  of  the  span,  the  ulti- 
mate breaking  load  of  a  continuous  beam  is  equal  to  twice  that 
for  a  non-continuous  beam  similarly  loaded  and  of  the  same 
length  and  section. 

When  the  load  is  evenly  distributed,  the  ultimate  load  for  a 
continuous  beam  is  1.5  times  greater  than  the  ultimate  load  for 
a  non-continuous  beam  under  the  same  conditions  and  of  the 
same  length  and  section. 

The  deflection  of  a  continuous  beam  is  one-fourth  that  of  a 
non-continuous  beam  when  similarly  loaded. 

To  find  the  strength  and  stiffness  of  continuous  beams,  take 
the  rules  given  for  non -continuous  beams  and  alter  the  co-efficients 
in  the  proportions  stated. 

EXAMPLES  FOR  CONTINUOUS  BEAMS. 

A  4-inch  I  beam  of  three  square  inches  section  is  continuous 
over  supports  twenty  feet  apart.  To  find  the  greatest  safe  load 
uniformly  distributed,  and  corresponding  deflection,  take 
1.5  times  the  co-efficient  for  a  similar  non-continuous  beam. 

— ^ =•  3 . 78  tons  breaking  load,  or  1 . 26  tons  safe  distrib- 
uted load.  For  deflection,  take  four  times  the  co-efficient  for  the 

same  class  of  non-continuous  beam.     ^ — i ^  =  0.58  of  an 

360  x  3  x  16 

inch  deflection. 
For  a  continuous  beam  bearing  load  in  middle,  take  twice  the 


76 


WROUGHT  IRON  AND   STEEL. 


co-efficient  given  for  the  strength  of  a  similarly  loaded  non-con- 
tinuous beam,  and,  for  deflection  of  the  former,  take  four  times 
the  co-efficient  given  for  the% latter  beam. 

It  will  be  observed  that  these  rules  apply  only  to  the  interme- 
diate spans  of  continuous  beams,  as,  owing  to  the  failure  of  con- 
tinuity at  one  end  of  each  outer  span,  the  conditions  are  altered. 
If,  however,  the  outer  ends  of  a  continuous  beam  overhang  the 
end-supports  from  one-fifth  to  one-fourth  of  a  span,  and  bear  the 
same  proportion  of  load  as  the  parts  between  supports,  then  the 
outer  spans  may  be  of  same  length  as  the  intermediate  spans, 
subject  to  the  same  load,  and  the  strength  and  stiffness  are  de- 
termined by  the  same  rules  ;  otherwise,  the  outer  spans  ought 
to  be  only  four-fifths  of  the  length  of  the  intermediate  spans 
when  the  load  is  distributed,  or  three-fourths  of  the  same  when 
the  load  is  concentrated  in  the  middle  ;  or,  if  the  lengths  of 
spans  are  all  alike,  the  loads  on  outer  spans  ought  to  be  reduced 
in  the  same  proportion. 

The  following  table  exhibits  the  relative  proportions  of 
strength  and  stiffness  existing  between  the  various  classes  of 
beams  when  they  have  the  same  lengths  and  uniform  cross 
sections  ;  the  deflections  being  comparative  figures  for  the  same 
loads. 


KIND  OF  BEAM. 

Breaking 
loud  as 

Deflection 
as 

Fixed  at  one  end  —  loaded  at  the  other 

l 

16 

Fixed  at  one  end  —  load  evenly  distributed.  .  . 

* 

6 

Supported  at  both  ends  —  load  in  middle  

1 

1 

Supported  at  both  ends  —  load  evenly  distrib- 
uted   

2 

| 

Continuous  beam  —  load  in  middle    

2 

i 

Continuous  beam  —  load  evenly  distributed.  .  . 

3 

R 
ft 

The  breaking  load  and  deflection  of  a  beam  supported  at  both 
ends  and  loaded  in  the  middle  have  been  taken  as  the  units  in 


EXAMPLES   FROM  PRECEDING   TABLES. 


77 


the  preceding  table,  and — the  proportional  strength  and  stiffness 
of  similar  beams  under  different  conditions  given — to  find  the 
proper  co-efficient  for  estimating  the  strength  and  stiffness  of 
the  beam  required,  it  is  necessary  to  alter,  in  the  given  propor- 
tions, the  co-efficient  for  the  same  beam  when  supported  at  both 
ends  and  loaded  in  the  middle. 


CHANGES  OF  CO-EFFICIENTS  FOR  SPECIAL  FORMS  OF 
BEAMS. 

For  beams  of  the  character  denoted  in  list  below,  change  the 
co-efficients  in  table  of  formulae,  pages  68-69,  in  the  ratio  given. 
For  concentrated  loads  and  distributed  loads  respectively, 
change  the  co-efficients  given  for  the  same  kinds  of  loads  in  the 
table. 


KIND   OF  BEAM. 

CO-EFFICIENT  FOR 
ULTIMATE  LOAD. 

CO-EFFICIENT  FOB 
DEFLECTION. 

Fixed  at  one  end,  loaded  at 
the  other. 

One-fourth  (\)  of 
the  co-efficient  of 
table. 

One  -  sixteenth 
(A-)  of  the  co- 
efficient of  ta- 
ble. 

Fixed  at  one  end,  load 
evely  distributed. 

One-fourth  (\)  of 
the  co-efficient  of 
table. 

Five  -  forty- 
eighths  (-&)  of 
the  co-efficient 
of  tables. 

Both  ends  rigidly  fixed,  or 
a  continuous  beam, 
with  load  in  middle. 

Twice  the  co-effi- 
cient of  table. 

Four  times  the 
co-efficient  of 
table. 

Both  ends'  rigidly  fixed,  or 
a  continuous  beam,  with 
load  evenly  distributed. 

One  and  one-half 
(1?)  times  the  co- 
efficient of  table. 

Four  times  the 
co-efficient  of 
table. 

78 


WKOUGHT  IBON  AND   STEEL. 


BENDING  MOMENTS  AND  DEFLECTIONS  FOR  BEAMS 
OF  UNIFORM  SECTION. 


W=  Total  load. 

L  =  Length  of  beam. 


E  =  Modulus  of  elasticity. 
/  =  Moment  of  inertia. 


FORM  OP  BEAM  AND  POSITION  OF 
LOAD. 

Maximum 
bending 
moment. 

Maximum 
shearing 
stress. 

Deflection. 

Beam  fixed  at  one  end  loaded  at  the 
other  : 

+  r\      F|G-  1 

^ 

^^N. 

at  point  of 
support 

at  point  of 
support 

at  end  of 
beam 

i 

(w) 

~  3£7" 

Draw  triangle  having  A  =  WL. 
Vertical  lines  give  bending  moments 
at  corresponding  points  on  the  beam. 

Beam  fixed  at  one  end,  load  uni- 
formly distributed  : 

7  N. 

|         ! 

G.  2 

at  point  of 
support 

2  ' 

at  point  of 
support 

at  end  of 
beam 
_  WL* 

^Lo  o  o  o  o_o 

Draw  pnrabola  having  A  =  —  k  — 

Ordinates  give  bending  moments  at 
corresponding  points  on  the  benm. 

Beam  supported 
ed  in  the  middle  : 

at  both  ends,  load- 

,/j 

v          FIG.  3 

>  IV 

1   T\ 

at  middle 
of  beam 
_  WL 

4  ' 

at  point  of 
support 

=  "2" 

at  middle 
of  beam 
'._  WL* 

<_  L                (g)                     -» 

Draw  triangle  having  A  =  

Vertical  lines  give  bending  moments 
at  corresponding  points  on  the  beam. 

BENDING  MOMENTS  AND  DEFLECTIONS. 


79 


BENDING  MOMENTS  AND  DEFLECTIONS  FOR  BEAMS 
OF  UNIFORM  SECTION. 


W=  Total  load. 

L  =  Length  of  beam. 


E  =  Modulus  of  elasticity. 
/  =  Moment  of  inertia. 


FORM  OP  BEAM  AND  POSITION  OP 
LOAD. 

Maximum 
bending 
moment. 

Maximum 
shearing 

stress. 

Deflection 

Beam  supported  at  both  ends,  load 

uniformly  distributed  : 

x^T^x'4 

at  middle 

at  point  of 

at  middle 

/                  ^           '  ^\v 

of  he-am 

support 

of  beam 

A                              i\ 

WL 

W 

WL3 

/  1                     !    !  \ 

8    ' 

~  2' 

~  76.8.E7' 

WL 

Draw  parabola  having  A  =  — 

o 

Ordinates  eive  bending  moments  at 
corresponding  points  on  the  beam. 

Beam  supported  at  both  ends,  load 
concentrated  at  any  point  : 

at  point  of 

support 

next  to  a 

/  \v.                FIG>  5 

_  Wb 

at  position 
of  load 

L  ' 

at  position 
of  load 

A                               '  ^^\^ 

Wab 

at  point  of 

a262  W 

S\                             j           !          '          !\^ 

L 

support 

~  3EIL' 

;::::  1  ©~  "       -H 

_  Wa 

Wab 

Draw  triangle  having  A  =  . 
L 

Vertical  lines  give  bending  moments 
at  corresponding  points  on  the  beam. 

80 


WKOUGHT  IRON  AND   STEEL. 


BENDING  MOMENTS  AND  DEFLECTIONS  FOR  BEAMS 
OF  UNIFORM  SECTION. 


W  =  Total  load. 

L  =  Length  of  beam. 


E  =  Modulus  of  elasticity. 
/  =  Moment  of  inertia. 


Beam  supported  at  both  ends,  with  concentrated  load  at  various  points  : 
R  FIG.  6 


Draw  (by  5)  the  triangles  having  vertices  at  C,  D  and  E,  the  verticals  rep- 
resenting bending  moments  for  loads  w1,  w*  and  w3,  respectively.  Extend 
FC  to  P,  GD  to  R,  and  HE  to  S,  making  each  long  vertical  equal  to  the  sum 
of  the  bending  moments  corresponding  to  its  position.  That  is,  FP  =  FO 
+  FI+  FJ.  GR  =  GD  +  GL  +  GK.  And  HS  =  HE+  HN+  HM.  Verti- 
cals drawn  from  any  point  on  the  polygon,  APBSB  to  AB,  will  represent  the 
bending  moments  at  the  corresponding  points  on  the  beam. 


Beam  rigidly  secured  at  each  end,  and  loaded  in  the  middle.  Or  the  inter- 
mediate spans  of  a  continuous  beam,  equally  loaded  in  the  middle  of  each 
span : 

A 


FIG.  7 


<-— L 


Points  of  contraflexure  at  #,  ce,  where  Moment  =  0.    Distance  of  x  from 
either  support  =  —  .  Equal  moments  at  middle  and  ends  =  —  —  . 
WL* 


WL 


Deflection 


—j-'  and  at  ends  draw  verticals  BB',  each 


Draw  a  triangle  having  A 

=  ^p'  join  BB'.    The  vertical  distances  between  BB'  and  the  sides  of  the 
triangle,  represent  the  moments  for  corresponding  points  en  the  beam. 


BENDING  MOMENTS  AND  DEFLECTIONS. 


81 


BENDING  MOMENTS  AND  DEFLECTIONS  FOR  BEAMS 
OF  UNIFORM  SECTIONS. 


W  =  Total  load. 

L  =  Length  of  beam. 


E  =  Modulus  of  elasticity. 
/  =  Moment  of  inertia. 


Beam  rigidly  secured  at  each  end  with  load  uniformly  distributed. 
Or  the  intermediate  spans  of  a  continuous  beam  bearing  a  uniformly  dis- 
tributed load  on  each  span  : 

FIG.  8 


Points  of  contraflexure  x,  x,  where  moment  =  0.    Distance  of  x  from 
either  support  =  .21  L. 

Draw  parabola  having  A  =  -5—    Draw  verticals  B,  E',  each  equal  to 

O 
TTTr 

— -p join  BE',    The  vertical  distances  between  BE'  and  the  curve  of  the  pa- 
rabola represent  the  moments  for  corresponding  points  on  the  beam. 

WL 

Maximum  moment  at  points  of  support  =  -r~-. 


Moment  at  middle  of  beam  = 


WL 


Maximum  deflection  at  middle  of  beam 


WL* 
307. 2£7* 


82  WROUGHT  IRON  AND   STEEL. 

BEAMS  FOR  SUPPORTING  IRREGULAR  LOADS. 

When  a  beam  has  its  load  unequally  distributed  over  it,  the 
proper  size  of  the  beam  can  be  determined  by  finding  the  maxi- 
mum bending  moment  and  proportioning  the  beam  accordingly. 
Equilibrium  is  obtained  when  the  bending  moment  is  equal  to 
the  moment  of  resistance.  That  is,  when  the  external  force  mul- 
tiplied by  the  leverage  with  which  it  acts  is  equal  to  the  strength 
of  the  material  in  the  cross  section  of  the  beam  multiplied  by 
the  leverage  with  which  it  acts.  The  ultimate  moment  of  resist- 
ance for  a  wrought-iron  beam  of  symmetrical  form  is 

42000  /       84000_/ 
-£  depth  d 

d  =  depth  of  beam  in  the  direction  in  which  the  force  acts. 
1=  the  moment  of  inertia  about  the  axis  at  right  angles  to  the 

direction  of  the  force. 

The  greatest  sai'e  moment  of  resistance  as  adopted  in  our  tables 
is  one-third  (j)  of  above, 

^_  280007  M        I 

~  ' 


38000"^ 

The  co-efficient  to  be  changed  according  to  the  factor  of  safety 

desired.    The  rule  would  thus  be    '  -  =  -  • 

Co-efficient      d 


RULE  FOR  BEAMS  BEARING  IRREGULAR  LOADS. 

Find  by  the  methods  described  in  preceding  article  the  maxi- 
mum bending  moment  in  inch-lbs.  for  the  loads.  Divide  the 
moment  by  the  proper  co-efficient  as  described  above.  Find  in 
the  tables,  pages  92-96,  a  beam  whose  inertia  divided  by  its 
depth  is  not  less  than  this  quotient;  which  will  be  the  beam  re- 
quired. 

In  some  instances  the  maximum  bending  moment  can  be  most 
readily  found  by  the  use  of  diagrams,  as  described  in  the  succeed- 
ing article. 

When  this  is  done  use  any  convenient  scale,  making  all  loads 


RULES  FOB  BEAMS  BEARING  IRREGULAR  LOADS.  83 

and  all  distances  respectively  of  the  same  denominations.     The 
maximum  bending  moment  can  then  be  measured  to  scale. 

Example.  —  An  I  beam  8  feet  long  is  to  be  fixed  at  one  end  and 
loaded  at  the  other  with  5,000  Ibs.  and  carrying  also  an  evenly 
distributed  load  of  8,000  Ibs.  What  size  of  beam  should  be  used 
so  as  not  to  ba  strained  over  one-third  of  its  ultimate  capacity  ? 

Moment  for  end  load  =  5,000  x  96  =  480,000  inch-lbs. 

"    distributed  load  =  8>00°  '  x  96  =  384,000      " 

A  __ 

Total  =  864,000      " 
For  one-third       of  ultimate  the  co-efficient  will  be 


28,000. 


864.000  J 

28,000  -  ~d 


By  Column  VII.,  page  92,  for  a  12"  168  Ib.  I  beam,  J  = 
371.98,  which  divided  by  12  =  30.99;  or  a  15"  145  Ib.  I  beam, 

-5-  =34.7.     The  latter  beam  would  be  stronger  and  lighter. 

In  the  following  example  the  maximum  bending  moment  can 
be  very  readily  obtained  by  a  diagram  as  described  in  Fig.  6  of 
the  preceding  article. 

Example.  —  A  beam  20  feet  long  between  supports,  will  carry 
three  loads,  which  we  will  call  A,  B,  and  C. 

A  —  4,000  Ibs.  and  is  4  feet  from  one  end  of  the  beam. 
C  —  6,000  Ibs.  and  is  3  feet  from  the  other  end  of  the  beam. 
B  =  5,000  Ibs.  and  is  5  feet  from  C  and  8  feet  from  A. 

What  beam  is  best  to  use  for  above,  not  strained  over  one- 
fourth  of  the  ultimate  ?  Describe  the  diagram  as  per  Fig.  6, 
when  the  following  bending  moments  in  ft.  -Ibs.  will  be  ob- 
tained. 


WROUGHT   IRON   AND    STEEL. 


At  point  A 

For  load  4..  12,800 
B..    8,000 
C.:    3,600 

At  point  B 

For  load  B..  24,000 
A..  10,800 
C.  .    6,400 

At  point  C 

For  load  C.  .  15,300 
B..    8,900 
A..    2,400 

Total  24,400 

Total....  41,200 

Total.  .  .  .  26,600 

The  maximum  moment  at  B  =  41,200  ft.-lbs.  or  494,400  inch. 
Ibs.     For  one-fourth  of  ultimate  strength  co-efficient  =  21,000. 


494.400 
21,000 


=  23.5  =  V 


By  table  on  page  92,  for  a  12"  120  Ib.  I  beam  L  =  22.74,  be- 

d 

ing  slightly  deficient.     A  12"  125  Ib.  I  beam  will  be  ample. 

If  more  lateral  stiffness  is  required  than  a  single  beam  affords, 
use  a  pair  of  channels  separated  and  braced  horizontally.  Two 

12"  75  Ib.  channels  -j  =  23.6,  would  suit  above  purposes. 

NOTE. — The  tables  of  elements,  except  where  otherwise  speci- 
fied, are  calculated  for  dimensions  in  inches  and  weights  in  Ibs., 
consequently  in  examples  of  above  character  it  is  necessary  to 
obtain  bending  moments  in  inch-lbs. 


BEAMS  SUBJECT  TO  BOTH  BENDING  AND  COM- 
PRESSION. 

When  a  beam  is  subjected  to  bending  action  and  simulta- 
neously has  to  act  as  a  strut  by  resisting  compression,  the  stress 
of  the  fibres  of  the  beam  in  tension  will  be  relieved  and  those  in 
compression  correspondingly  augmented. 

No  general  rules  can  be  given  for  such  conditions,  as  every 
particular  case  requires  its  own  proper  determination.  The  fol- 
lowing methods,  though  not  strictly  correct,  will  give  safe  re- 
sults for  some  simple  forms  of  trussed  girders,  etc. 

(1.)  When  the  beam  is  subject  to  compression  but  is  so  con- 
fined laterally  that  it  cannot  fail  by  bending  like  a  strut. 


BEAMS  SUBJECT  TO  BENDING  AND  COMPRESSION.    85 

Rule. — Find  the  section  of  beam  required  to  resist  bending, 
then  allowing  from  10,000  to  15,000  Ibs.  per  square  inch  of  sec- 
tion for  the  compression,  according  to  the  factor  of  safety  used, 
add  the  area  so  found  to  the  first  area,  which  will  give  the  sec- 
tion of  required  beam. 

Example. — What  I  beam  is  required  to  span  an  opening  of  30 
feet,  to  be  trussed  3  feet  deep  between  centres  in  the  manner 
illustrated  in  Fig.  6,  page  165?  (this  trussed  beam  carries  a  brick 
wall  which  weighs  500  Ibs.  per  lineal  foot,  but  which  braces  the 
beam  from  yielding  sideways),  the  beam  to  be  proportioned  for 
a  safety  factor  of  four  ? 

Here  the  beam  can  be  considered  as  composed  of  two  separate 
beams,  reaching  from  the  centre  to  each  end,  each  being  15  feet 
long,  carrying  a  distributed  load  of  15  x  500  =  7,500  Ibs.,  and 
subject  to  a  compression  resulting  from  the  trussing  of  18,750 
Ibs.  Our  approximate  tables  for  beams,  on  page  69,  will  be 
found  most  convenient  for  such  calculations  as  the  above,  and 
are  sufficiently  accurate  for  practical  purposes.  For  I  beam, 

dividing  co-efficient  by  4  we  have     '      —  =  safe  distributed 


load  =  3. 75  tons. 

By  trial  we  find  for  an  8"  65  Ib.  I  beam  ltQ°  *®'5  *-  =  3.64, 

10 

or  nearly  correct. 

For  the  compression,  allowing  12,500  Ibs.  per  square  inch,  we 
require  l£  square  inches.  Therefore  an  8"  I  beam,  8  square 
inches  section,  will  be  safe. 

If  desirable  to  use  a  deeper,  lighter  beam,  try  a  9-inch  beam  75 
Ibs.  per  yard  ;  allowing  1|  square  inches  for  the  compression,  we 

have  a  section  of  6  square  inches  remaining  ;    — =  3.78. 

15 

The  latter  beam  being  both  stronger  and  lighter  than  the  8- 
inch. 

(2.)  When  the  beam  is  subject  to  compression  and  is  liable  to 
fail  like  a  horizontal  strut  by  lateral  flexure. 

Rule. — Consider  first  the  resistance  as  a  strut  and  then  make 
the  necessary  increment  of  section  to  resist  the  bending  stress, 
remembering  that  if  the  addition  is  made  to  the  flanges  then 
only  flange  stresses  have  to  be  considered,  but  if  the  increased 


86  WROUGHT  IRON  AND   STEEL. 

area  is  obtained  by  thickening  the  web  of  I  beam  or  channel  sec- 
tions,  then  the  additional  area  so  obtained  should  be  treated  as  a 
rectangular  section  whose  thickness  is  the  amount  added  to  the 
web,  and  whose  depth  is  the  depth  of  the  beam. 

Example.— A.  trussed  girder  of  the  form  exhibited  in  Fig.  8, 
page  165,  is  a  box  section  made  up  of  two  channels  separated  with 
flanges  outward,  and  plated  top  and  bottom.  The  whole  girder 
is  30  feet  long  and  is  loaded  1,000  Ibs.  per  lineal  foot.  The  com- 
pression resulting  from  the  trussing  is  25,000  Ibs.  The  structure 
has  no  lateral  bracing.  What  will  be  safe  proportions  for  it,  the 
stresses  not  to  exceed  £  of  the  ultimate  ? 

It  is  evident  that  we  have  to  consider  it  as  a  flat-ended  strut 
30  feet  long  liable  to  fail  horizontally,  and  also  as  a  series  of  3 
beams  each  10  feet  long  and  loaded  with  10,000  Ibs.  evenly  dis- 
tributed. Trying  2  lightest  5"  channels,  each  2.27  square  inches 
section,  separated  5£"  so  as  to  be  covered  by  9"  plates,  we  have 
(omitting  the  plates  in  this  calculation,)  the  radius  of  gyration 
around  vertical  axis  (see  page  110)  =.3.25  inch- 

l 
es,  -  =  110,  one-fifth  of  ultimate  (by  Table  I, 

page  118)  -  5,600  Ibs.  per  square  inch,  or  5,600 
x  4i  =  25,200  Ibs.  safe  resistance,  which  is 
ample.  Now  proportioning  the  plates  to  resist 
the  bending  strain  we  have  maximum  bend- 


1 9ft  v  1 0  000 

ing  moments  (see  page  78),    ~— 0  -'—  =  150,000  inch-lbs. 

o 

The  plates  act  with  a  leverage  equal  to  the  depth  of  the  chan- 
nel, viz.,  5";    — '-——  =  30,000  Ibs.  tension  on  top  or  compres- 
5 

sion  on  bottom  plate,  which,  allowing  for  10,000  Ibs.  per  square 
inch,  and  allowing  for  loss  by  rivets,  will  require  a  plate  f" 
thick. 

(3 )  Taking  the  last  example,  if  it  was  desired  to  form  the  sec- 
tion out  of  a  pair  of  channels  latticed  top  and  bottom  with  no 
cover  plates,  we  would  have  to  consider  the  section  added  to  the 
channels  (being  on  the  web  alone),  as  a  simple  rectangular  sec- 
tion. By  the  formula  on  page  69,  approximate  rules,  we  find 
that  such  a  section  only  5"  deep  would  require  a  thickness  of 
3.8  inches,  which  is  impracticable ;  we  have  therefore  to  use  deep- 


ELEMENTS  OF  PENCOYD  STRUCTURAL  SHAPES.      87 

er  and  heavier  channels.     Trying  8"  channels  separated  as  be- 
fore 5£  inches,  with  flanges  outward,  and  having  radius  of  gyra- 

tion for  the  pair  around  vertical  axis  =  3.4,  —  =  106.     Safe  load 

90  nftft 

^J>  1W=  5,800  Ibs.  per  square  inch.     As  the  compression  is  25,OCO 
5 

Ibs.,  there  is  required  4.8  square  inches  for  this  purpose.     By 


formula  2,  page  68,  -52  x  ^ea  x  8  _  5  tons,   from  which  is 

found  the  area  required  to  resist  bending  —  12  square  inches. 
12  4-  4.3  =  10.3  square  inches  for  2  channels,  or  the  heaviest  8 
channels  80  Ibs.  per  yard  would  be  required. 

By  the  same  method  we  find  10"  channels  68  Ibs.  per  yard, 
will  answer  the  purpose,  or  our  lightest  12"  channels  60  Ibs. 
per  yard,  will  exactly  meet  the  requirements  and  be  the  lightest 
channel  that  can  be  used  in  the  manner  proposed  for  the  pur- 
pose. 

In  cases  where  the  load  is  concentrated  at  the  truss  points, 
there  being  no  bending  stress,  the  resistance  as  a  strut  has  only 
to  be  considered,  and  when  braced  laterally  the  strut  length  is 
reduced  to  the  distances  between  bracir.g. 


ELEMENTS  OF  PENCOYD  STRUCTURAL  SHAPES. 

In  the  following  tables,  pages  88,  91,  various  properties  of 
rolled  structural  iron  are  given,  whereby  the  strength  or  stiff- 
ness of  any  shape  can  be  readily  determined. 

SYMBOLS. 

I  =  Moment  of  inertia. 
E  —  Modulus  of  elasticity. 
W  •=  Load  on  beam  in  net  tons. 
w  =  Load  on  beam  in  pounds, 
R  =  Radius  of  gyration. 
A  —  Total  area  of  cross  section. 
L  —  Length  between  supports  in  feet. 

I  =  Length  between  supports  in  inches. 


88  WROUGHT   IRON  AND  STEEL. 

Column  I. — Chart  number. 

Columns  III.  to  VI. — Details  of  the  sectional  areas  in  square 
inches.  The  flanges  being  taken  the  entire  width 
of  section,  and  the  web  considered  between  the 
flanges. 

Columns  VII.  and  VIII. — The  moments  of  inertia,  respectively, 
at  right  angles  to  and  parallel  with  web  of  beam. 
In  all  cases  the  axes  referred  to  pass  through  the 
centre  of  gravity  of  the  cross-section,  as  illustra- 
ted at  the  head  of  each  table. 

Columns  IX.  and  X. — The'  radii  of  gyration  in  inches  —  A/  —. 

r    A 

When  R2  is  required,  simply  divide  the  moment 
of  inertia  by  the  area  of  the  section.  The  values 
of  /  and  R  have  all  been  carefully  calculated  by 
the  formulae  given  on  pages  102-111.  The  tables 
give  the  value  of  1  for  the  minimum  section 
of  each  particular  shape,  but  the  section  can 
be  increased  in  area  up  to  the  maximum  limit 
given  in  the  descriptive  tables,  pages  2-12, 
and  the  value  of  /  can  be  readily  obtained 
for  any  enlarged  section  as  described  on  pages 
106-108. 

Column  XI. — Co-efficient  for  the  greatest  safe  load  evenly  dis- 
tributed over  the  beam.  This  is  the  calculated 
load  in  net  tons  for  a  beam  of  the  given  size  and 
section,  one  foot  long,  and  is  derived  from  the 

formula  --  =  — — — — — -,  which  gives  re- 

8       £  depth  of  beam 

suits  averaging  one-third  of  the  ultimate  strength 
of  the  beam.  The  safe  distributed  load  for  any 
beam  of  the  size  and  section  given  in  Columns  II. 
to  VI.  can  be  found  by  dividing  the  correspond- 
ing co-efficient  in  column  XI.  by  the  length  of 
the  beam  between  supports,  in  feet. 

Example. — The  greatest  safe  load  that  can  be  evenly  distrib- 
uted on  a  beam  10  inches  deep  having  a  sectional  area  of  9.04 

"1  Qft   A. 

square  inches  and  spanning  12  feet  is     10'   =  11.5  tons. 


ELEMENTS  OF  PENCOYD  STRUCTURAL  SHAPES.  89 

If  -the  load  is  concentrated  in  the  middle  of  the  beam,  one- 
half  this  result,  or  5.75  tons,  is  the  greatest  safe  load. 

If  the  sectional  area  of  the  beam  is  increased,  find  the  moment 
of  inertia  for  the  increased  section  as  described  on  page  106,  and 

the  co-efficient  for  a  distributed  safe  load  =  -  -  -3-  _  . 

depth  of  beam 

Example.  —  The  10"  beam  taken  in  last  example,  9.04  square 
inches  area,  is  increased  to  10.6  square  inches  section.  The  in- 
ertia of  enlarged  section  is  found  as  per  formula  on  page  106, 
1.56  =  (increase  of  area)  x  100  =  (square  of  depth)  10 

-  -  -  ~j  -  =  -  =  -  -  =  lo.  +  1  4o  .  o 

I/O 

(inertia,  col.  vii.,  page  92,)  —  161  .3  or  moment  of  inertia  desired. 
Co-efficient  for  safe  load  =  161>  ^  >  -^  =  150.5.  Dividing  this 

co-efficient  by  the  span  in  feet  (12),  gives  -^f~  =  12.54  tons  as 

\4i 

the  maximum  safe  load  distributed,  or  6.27  tons  in  the  middle  of 
the  beam. 

Lateral  Flexure.  —  It  will  be  noted  that  when  subjected  to  such 
loads  as  above  obtained,  the  beams  are  presumed  to  be  secured 
from  bending  sideways,  and  it  will  be  safest  to  limit  the  applica- 
tion to  beams  secured  laterally  at  intervals,  in  length  not  ex- 
ceeding twenty  times  the  width  of  flange.  See  preface  to  tables 
of  safe  loads  for  beams,  page  36. 

Columns  XII.  and  XIII.  —  Deflections. 

The  figures  in  the  tables  are  the  calculated  deflections  for 
beams  of  the  sizes  and  sections  given,  one  foot  long  between 
bearings  and  supporting  a  load  of  one  ton.  They  are  derived  by 

means  of  the  formulae     X   =  deflection  for  load  in  middle  of 


beam.     ^  =  deflection  for  load  evenly  distributed. 

7o  . 


The  modulus  of  transverse  elasticity  is  assumed  as  26,000,000 
Ibs.  The  elasticity  of  rolled  iron  is  somewhat  uncertain,  it  is 
frequently  quoted  as  high  as  29,000,000  Ibs.,  and  experiments 
on  bars  of  exceptionally  stiff  iron  will  often  give  results  much  in 
excess  of  this.  But  recent  experiments  on  rolled  beams  show 
that  26,000,000  Ibs.  is  a  fair  average  for  this  form  of  wrought 
iron.  See  page  19. 


90  WROUGHT  IRON    AND    STEEL. 

The  deflection  of  any  beam  of  the  sectional  area  given  in  cols. 
IV.  to  VI.,  and  loaded  within  the  elastic  limit,  is  found  by  mul- 
tiplying the  corresponding  co-efficient  in  cols.  XII.,  XIII.,  by 
the  weight  in  tons  and  the  cube  of  the  length  in  feet. 

Example.— A.  12"  I  beam,  11.95  square  inches  section,  13  feet 
between  supports,  carries  an  evenly  distributed  load  of  15  tons. 
Deflection-  .0000063  x  15  x  133  =  .207  inches. 

If  the  sectional  area  of  this  shape  is  increased,  the  value  of  1 
for  the  enlarged  section  must  be  found  as  described  in  previous 
example.  By  reducing  the  formulae  for  deflection  to  their  sim- 
plest forms  we  obtain  : 

1 1  r  T  :< 

=  deflection  in  inches  for  load  in  middle. 


3627 

"WJ  'J 

=-^4-  =  deflection  in  inches  for  distributed  load. 
5807 

Example. — The  12"  beam  in  previous  example  11.95  square 
inches  area,  is  increased  to  13.8  square  inches     The  inertia  of 
enlarged  section  is  found  as  per  formula,  page  106. 
1 . 85  (increase  of  area)  x  144  (square  of  depth)  _ 

-i  n  —  **  •  *     l~  *  *•»«  ~" 

inertia,  col.  vii.,  page  92,  =  295.06,  or  moment  of  inertia  desired. 


For  beams  of  the  same  depth,  but  of  any  sectional  area,  thts 
deflection  remains  uniform  so  long  as  the  loads  bear  a  uniform 
ratio  to  the  strength  of  the  beam.  For  this  reason,  the  single 
column  of  deflections  applies  to  any  section  of  the  same  size  of 
beam,  in  the  tables  of  safe  loads. 

Column  XIV. — Maximum  load  in  tons. 

There  is  a  limit  in  the  length  of  beams  at  which  the  rule  for 
safe  loading  ceases  to  apply.  This  point  is  reached  when  the 
load  attains  the  safe  limit  of  resistance  offered  by  the  web  of  the 
beam  against  crippling. 

The  maximum  load  can  be  placed  on  any  beam  shorter  than 
the  length  indicated,  but  must  not  be  exceeded.  It  is  obtairied 
by  Gordon's  formula,  taking  6  tons  per  square  inch  as  the  safe 
resistance  of  wrought  iron  to  crushing. 


ELEMENTS  OF  PENCOYD  STBUCTUBAL  SHAPES.  91 

W  =       6^  d  =  depth  of  beam, 

-j    ,       P  t  —  thickness  of  web. 

3000^  I  =  d  x  secant  45°  (P  =  2cf). 

Example. — An  8"  65  Ib.  beam  has  a  maximum  load  of  10.46 
tons,  which  corresponds  to  the  greatest  safe  load  on  a  beam  of 
this  section,  7.7  feet  between  supports,  if  the  load  is  distributed, 
or  3.85  feet  if  the  load  is  at  middle  of  beam.  If  this  shape  is  in- 
creased to  7-i  square  inches  area,  having  a  web  -fc"  thick,  then 
maximum  safe  load  becomes 

6"  x  8"  x  -i 


92  WROUGHT  IRON  AND  STEEL. 

ELEMENTS  OF  FENCOYD  BEAMS. 


r 


I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

CHART 
NUM- 
BER. 

1 

SIZE 

IN 

INCHES. 

WEIG'T 

PER 

YARD. 

AREAS  IN  SQUARE  INS. 

MOMENT  OP  INERTIA. 

Flanges 

Web. 

Total. 

Axis  A.  B. 

Axis  C.  D. 

15 

200 

11.86 

8.04 

19.90 

682.08 

28.50 

2 

15 

145 

8.97 

5.58 

14.55 

521.19 

16.91 

3 
4 
5 

12 
12 

m 

168 
120 
134 

10.66 

7.42 
9.57 

6.23 
4.53 

3.87 

16.89 
11.95 
13  44 

371.98 

272.86 
241.63 

23.19 
12.22 
19.00 

5* 

104 

108 

7.33 

3.50 

10.83 

195.42 

12.45 

6 

10* 

89 

5.91 

3.03 

8.94 

162.26 

8.34 

7 

10 

112 

7.23 

3.94 

11.17 

173.58       10.64 

8 

10 

90 

6.29 

2.75 

9.04 

148.31 

8.09 

9 

9 

90 

6.15 

2.92 

9.07 

118.81 

8.44 

10 

9 

70 

4.77 

2.21 

6.98 

94.44 

5.59 

11 

8 

81 

5.58 

2.56 

8.14 

83.93 

7.23 

12 

8 

65 

4.50 

2.03 

6.53 

69.17 

5.02 

13 

7 

65 

4.17 

2.41 

6.58 

49.78 

4.15 

14 

7 

52 

3.84 

1.30 

5.14 

43.08 

3.43 

15 

6 

50 

3  16 

1.88 

5.04 

26.92 

2.15 

16 

6 

40 

2.91 

1.17 

4.08 

24.10 

1.80 

17 

5 

34 

2.13 

1.25 

3.38 

13.40 

1.21 

18 

5 

30 

2.06 

.88 

2.94 

12.50 

1.09 

19 

4 

28 

2.15 

.75 

2.90 

7.69 

1.17 

20 

4 

18.5 

1.34 

.56 

1.90 

5.14 

.49 

21 

3 

23 

1.72 

.53 

2.25 

3.29 

.77 

22 

3 

17 

1.37 

.34 

1.71 

2.66 

.48 

ELEMENTS  OF  PENCOYD  BEAMS. 


93 


ELEMENTS  OF  PENCOYD  BEAMS. 


IX. 

X. 

XI. 

XII. 

XIII. 

XIV- 

li 
£ 

SIZE  IN  INCHES.  S 

CHART  1  ,_ 

•-*•  NUMBER. 

RADII  OF  GYRATION. 

CO-EFFICIENT 
SAFE  LOAD 
DISTRIBUTED. 

CO-EFFICIENT  FOR 
DEFLECTION. 

Axis  A.  B. 

Axis  C.  D. 

Load  in 
Centre. 

Load  Dis- 
tributed. 

5.86 

1.20 

424.41 

.  0000041 

.0000025 

43.20 

15 

5.98 

1.08 

324.30 

.0000053 

.0000033 

22.10 

15 

2 

4.69 

1.17 

289.32 

.0000074 

.0000046 

38.63 

12 

3 

4.78 

1.01 

212.22 

.0000101 

.OCOOC63 

22.22 

12 

4 

4.24         1.19 

214.78 

.0000115 

.0000072 

22.13 

101 

5 

4.25 

1.07 

173.71 

.OOC0142 

.0000089 

17.71 

101 

6i 

4.26 

.97 

144.23 

.0000171 

.0000107 

13.35 

104 

6 

3.94 

.98 

162.02 

.0000159 

.0000099 

23.68 

10 

7 

4.05 

.95 

138.43 

.0000186 

.0000116 

13.18 

10 

8 

3.62 

.96 

123.21 

.0000232 

.0000145 

16.53 

9 

9 

3.68 

.89 

97.94 

.0000292 

.0000183 

9.94 

9 

10 

3.21 

.94 

97.92 

.0000329 

.0000205 

15.49 

8 

11 

3.25 

.88 

80.70 

.0000099 

.0000249 

10.46 

8 

12 

2.75 

.79 

66.38 

.0000546 

.0000341 

15.69 

7 

13 

2.89 

.82 

57.44 

.0000640 

.0000400 

6.17 

7 

14 

2.31 

.65 

41.87 

.0001025 

.0000641 

12.77 

6 

15 

2.43 

.66 

37.49 

.0001144 

.0000715 

6.50 

6 

16 

1.99 

.60 

25.01 

.0002059 

.OC01C87 

8.01 

5 

17 

2.06 

.60 

23.33 

.0002206 

.0001379 

4.86 

5 

18 

1.63 

.63 

17.94 

.0003589 

.0002243 

5.12 

4 

19 

1.65 

.51 

12.00 

.C005366 

.0003354 

3.03 

4 

20 

1.21 

.59 

10.24 

.0008382 

.0005-239 

4.11 

3 

21 

1.25 

.53 

8.28 

.0010366 

.0006479 

2.34 

3 

22 

94:  WROUGHT  IKON  AND  STEEL. 

ELEMENTS    OF   FENCOYD    CHANNELS. 


I. 

CHART 

NUM- 
BER. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

SIZE 

IN 

INCHES. 

WEIO'T 

PER 

YARD. 

AREAS  IN  SQUARE  INS. 

MOMENTS  OP  INERTIA 

Flanges 

Web. 

Total. 

Axis  A.  B. 

Axis  C.  D. 

30 

15 

148 

6.50 

8.36 

14.86 

451.51 

19.05 

31 
32 

12 

12 

88.5 
60 

4.59 

2.87 

4.24 
3.07 

8.83 
5.94 

182.71 
123.71 

7.42 
3.22 

34 

10 

60 

3  5(5 

2.43 

5.99 

92.08 

4.2D 

35 

10 

49 

2.67 

2.22 

4.89 

73.91 

2.33 

36 

9 

54 

2.97 

2.43 

5.40 

64.34 

2.47 

37 

9 

37 

1.81 

1.91 

3.72 

43.65 

1.31 

38 

8 

43 

2.28 

1.97 

4.25 

40.00 

2.17 

39 

8 

30 

1.34 

1.62 

2.96 

28.23 

1.06 

40 

7 

41 

2.30 

1.80 

4.10 

29.51 

1.71 

41 

7 

26 

1.38 

1.26 

2.64 

18.46 

.90 

42 

6 

33 

2.04 

1.25 

3.29 

18.37 

1.46 

44 

6 

23 

1.09 

1.18 

2.27 

11.67 

.59 

45 

5 

27.3 

1.69 

1.04 

2.73 

10.29 

.86 

46 

5 

19 

.91 

.97 

1.88 

6.67 

.37 

47 

4 

21.5 

1.34 

.81 

2.15 

5.16 

.54 

48 

4 

17.5 

1.02 

.73 

1.75 

4.14 

.41 

49 

3 

15 

.86 

.66 

1.52 

2.03 

.32 

50 

ft 

11.3 

.69 

.44 

1.13 

.80 

.21 

51 

2 

8.75 

.55 

.33 

.88 

.48 

.08 

ELEMENTS   OF  PENCOYD   CHANNELS.  95 

ELEMENTS    OF    PENCOYD    CHANNELS. 


IX. 

x 

XI. 

XII. 

XIII. 

XIV. 

XV. 

II. 

I. 

RADII  OF 
GYRATION. 

Ill 

CO-EFFICIENTS  FOR 
DEFLECTION. 

p 

81? 

o 
M 

"si 

h       3 

Axis  Uxie 

W  fc  H 

6-"1  2 

Load  in 

Load  dis- 

||| 

tt 

og 

A.  B. 

C.  D. 

o*P 

centre. 

tributed. 

r 

i 

S 

02 

5.51 

1.13 

280.94 

.0000061 

.0000038 

40.64 

.95 

15 

30 

4.55 

.92 

142.11 

.0000151 

.OOOC094 

18.49 

.71 

12 

31 

4.56 

.74 

96.22 

.0000223 

.0000139 

9.14 

.62 

12 

32 

3.92 

.84 

85.94 

.0000298 

.0000186 

9.10 

.751 

10 

34 

3.89 

.61) 

68.98 

.0000374 

.0000234 

7.25 

.64 

10 

35 

3.45 

.68 

66.73 

.0000429 

.0000268! 

10.87 

.67! 

9 

36 

3.43 

.59 

45.27 

.0000632 

.0000395 

6.38 

.55 

9 

37 

3.06 

.71 

46.66 

.0000690 

.0000431 

8.77 

.60 

8 

38 

3.09 

.60 

32.94 

.0000977 

.0000611 

4.79 

.50 

8 

39 

2.68 

.65 

39.35 

.00009^5 

.0000584 

9.07 

.65 

7 

40 

2.64 

.58 

24.61 

.0001495 

.0000934 

3.42 

.48 

7 

41 

2.36 

.67 

28.58 

.0001501 

.0000938 

6.50 

.66 

6 

42 

1 

2.27 

.51 

18.16 

.0002363 

.0001477 

5.24 

.46 

6 

44 

1.93 

.56 

19.21 

.0002680 

.0001675 

5.92 

.61 

5 

45 

1.88 

.45 

12.45 

.0004136 

.0002585 

4.86 

.42 

5 

46 

1.55 

.50 

12.03 

.0005349 

.0003343 

5.12 

.53 

4 

47 

1.54 

.48 

9.65 

.0006667 

.0004167 

4.29 

.45 

4 

48 

1.16 

.46 

6.32 

.0013584 

.0008490 

3.49 

.51 

3 

49 

.85 

.43 

3.33 

.0034350 

.0021470 

3.20 

.46 

Si 

50 

.74 

.3! 

5 

.0057230 

.0035770 

2.49 

.37 

2 

51 

96  WROUGHT    IRON   AND    STEEL. 

ELEMENTS  OP  PENOOYD  DECK  BEAMS. 


-c- 

VJ                ~P 

-- 

J^-JB     r 

I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

CHART 

SIZE 

WEIO'T 

AREAS  m  SQUARE  INS. 

MOMENTS  OF  INERTIA 

NUM- 

IN 

PER 

1 

BER. 

INCHES. 

YARD. 

1 

Fl'ge 

1 

Bulb. 

Web. 

Total. 

Axis  A.  B. 

Axis  C.  D. 

60 

12 

104 

3.59 

2.89 

3.90 

10.38 

221.98 

9.33 

61 

11 

91 

3.26 

2.52 

3.28 

9.06 

164.09 

7.64 

62 

10 

80 

2.87 

2.19 

2.96 

8.02 

118.22 

6.13 

63 

9 

72 

2.50 

2.06 

2.61 

7.17 

84.77 

4.92 

64 

8 

61 

2.17 

1.85 

2.09 

6.11 

57.66 

3.63 

65 

7 

52 

1.86 

1.55 

1.80 

5.2-1 

34.40 

2.59 

66 

6 

42 

1.52 

1.28 

1.38 

4.18 

21.95 

1.64 

67 

5 

34 

1.22 

1.04 

1.11 

3.37 

12.04 

.98 

ELEMENTS   OF  PENCOYD  DECK  BEAMS.  97 

ELEMENTS  OF  FENCOYD  DECK  BEAMS. 


=OP_ 


IX. 

RAD 
GYRA 

Axis 
A.  B. 

X. 

[I  OF 
TION. 

Axis 
C.  D. 

.95 

XI. 

XII. 

XIII. 

XIV. 

XV. 

SIZE  IN  INCHES.  S 

I. 

CO-EFFICIENT 
SAFE  LOAD 
DISTRIBUTED. 

CO-EFFICIENTS  FOB 
DEFLECTION. 

MAXIMUM  LOAD 
IN  TONS. 

DISTANCE,  d, 
FROM  BASE  TO 
NEUTRAL  Axis. 

M 

S| 

60 

Load  in 
centre. 

Load  dis- 
tributed. 

4.62 

172.6 

.0000122 

.0000078 

18.50 

5.24 

12 

4.25 

.92 

139.5 

.0000168 

.0000105 

15.72 

4.68 

11 

61 

3.84 

.87 

110.3! 

.0000233 

.0000146 

15.26 

4.27 

10 

62 

3.44 

.83 

87.9 

.0000325 

.0000203 

14.63 

4.00 

9 

! 
63 

3.07 

.77 

67.3 

.0000478 

.0000299 

12.12 

3.50 

8 

64 

2.57 

.71 

45.8 

.0000802 

.0000501 

11.30 

3.20 

7 

65 

2.29 

.63 

34.2 

.0001257 

.0000785 

9.03 

2.65 

6 

66 

1.89 

.54 

22.4 

.0002291 

.0001432 

8.01 

2.22 

5 

67 

WROUGHT   IRON  AND  STEEL. 


ELEMENTS  OF 


PENOO  YD  ANGLES. 


EVEN  LEGS. 


I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

~1~ 

ca 

• 

MOMENTS  OF 

RADII  OF 

•»ss 

1 

S 

INERTIA. 

GYRATION. 

g'i^ 

1 

SIZE  IN  INCHES. 

|| 

Axis 

Axis 

Axis 

Axis 

ill 

•4 

^ 

A.  B. 

C.D. 

A.  B. 

C.D. 

120 

6    x  6    x  fe 

50.6 

17.68 

7.16 

1.87 

1.19 

1.66 

6x6x1 

110.0 

35.46 

15.00 

1.80 

1.17 

1.86 

121 

5    x  5    x  -j3^ 

41.8 

10.02 

4.16 

1.55 

l.OOj 

1.41 

5x5x1 

90.0 

19.64 

8.67 

1.48 

.98 

1.61 

122 

4    x  4    x   3- 

28.6 

4.36 

1.86 

1.24 

.81 

1.14 

4    x  4    x   | 

54.4 

7.67 

3.45 

1.19 

.80 

1.27 

123 

3i  x  3i  x  £ 

24.8 

2.87 

1.20 

1.07 

.70 

1.01 

3|  x  3*  x   fc 

39.8 

4.33 

1.85 

1.04 

.69 

1.10 

124 

3    x  3    x   i 

14.4 

1.24 

.51 

.93 

.60! 

.84 

3    x  3    x   f 

33.6 

2.62 

1.15 

.88 

.59 

.98 

125 

2f  x  2f  x   i 

13.1 

.95 

.39 

.85 

.78 

2|  x  2|  x   i 

25.0 

1.67 

.72 

.82 

!54 

.87 

126 

2£  x  24-  x   i 

11.9 

.70 

.29 

.77 

.50 

.72 

2|  x  2*  x   i 

22.5 

1.23 

.54 

.74 

.49 

.81 

127 

2^  x  2^  x   i 

2i  x  2i-  x  -ft 

10.6 

17.8 

.50 
.79 

.21 
.34 

.69 
.67 

.45 
.44 

.65 

.72 

128 

2    x  2    x  -fV 

7  1 

.27 

.11 

.62 

.40 

.57 

2    x  2    x    $ 

13.6 

.50 

.21 

.61 

.39 

.64 

129 

1|  x  1J  x  A 

6.2 

.18 

.08 

.53 

.36 

.51 

1|  x  1|  x    i 

11.7 

.31 

.14 

.51 

.35 

.57 

130 

$4  X  1-f  X   1% 

5.3 

.11 

.05 

.46 

.31 

.44 

14    X    1£    X     £ 

9.8 

.19 

.09 

.44 

.31 

.51 

131 

H  x  1\  x    i 

3.0 

.05 

.02 

.41 

.26 

.36 

H  x  li  x    i 

5.6 

.08 

.04 

.38 

.26 

.40 

132 

1       X    1       X     i 

2.3 

.02 

.01 

.29 

.20 

.30 

1     x  1     x   i 

4.4 

.04 

.02 

.29 

.20 

.35 

1 

ELEMENTS   OP  PENCOYD   ANGLES. 


99 


\ 


ELEMENTS  OF 


\A 


_F-.  PENCOYD  ANGLES. 


UNEVEN   LEGS. 


I. 

II. 

ni. 

IV. 

V. 

VI. 

VII. 

VIII. 

IX. 

X. 

XI. 

K 
w 

li 

MOM.  OF  INERTIA. 

RADII  OF 
GYRATION. 

DlST.  FROM 

BASE  TO 

.NEUT.AXES 

s 

SIZE  IN  INCHES. 

p 

Axis 

Axis 

Axis 

Axis 

Axis 

Axis 

d. 

3 

A.B. 

C.  D. 

E.  F- 

A.  B. 

C.  D. 

E.  F. 

O 

140 

6    x4    x-ffi 

41.8 

15.46 

5.60 

3.55 

1.92 

1.16 

.92 

1.96 

.96 

6    x  4    x   1 

90.0 

30.75 

10.75 

7.46 

1.85 

1.09 

.91 

2.17 

1.17 

141 

5x4x| 

32.3 

8.14 

4.66 

2.47 

1.59 

1.20 

.87 

1.53 

1.03 

5x4x1 

80.0 

18.17 

10.17 

6.10 

1.51 

1.18 

.86 

1.75 

1.25 

142 

5    x  3£  x   a. 

30.5 

7.78 

3.23 

1.95 

1.60 

1(3 

.80 

.61 

.86 

5     x  3^  x    £ 

58.1 

13.92 

5.55 

3.72 

1  55 

'.98 

.79 

.75 

1.00 

143 

5    x  3"  x   $ 

28.6 

7.37 

2.04 

1.42 

1.61 

.85 

.70 

.70 

.70 

5    x  3    x   | 

54.4 

13.15 

3.51 

2.58 

1.55 

.80 

.69 

.84 

.84 

144 

4*  x  3    x    i 

86.7 

5.50 

1.98 

1.27 

1.44 

.86 

.69 

.49 

.74 

4^  x  3    x   t 

43.0 

8.44 

2.98 

2.04 

1.40 

.83 

.68 

1.58 

.83 

145 

4    x  3J-  x   f 

26.7 

4.17 

2.99 

1.44 

1.25 

1.06 

.74 

1.20 

.95 

4    x:sf  x  f 

43.0 

6.37 

4.52 

2.34 

1.22 

1.03 

.73 

1.29 

1.04 

146 

4    x  3     x   f 

24.8 

3.96 

1.92 

1.10 

1.26 

.88 

.67 

1.28 

.78 

4x3x1- 

89  8 

6.03 

2.87 

1.69 

1.23 

.85 

.65 

1.37 

.87- 

147 

3£  x  3    x  £J 

81.2 

2.53 

1.72 

.86 

1.09 

.90 

.64 

1.07 

.82 

3i  x  3    x   § 

36.7 

4.11 

2.81 

1.49 

1.06 

.87 

.64 

1.17 

.92 

148 

3    x  2fc  x  ft 

16.2 

1.42 

.90 

.47 

.94 

.74 

.54 

.93 

.68 

3    x  2i  x   i 

25.0 

2.08 

1.30 

.72 

.91 

.72 

.54 

1.00 

.75 

149 

,3    x  2    x   i 

11.9 

1.09 

.39 

.25 

.96 

.68 

.4(5 

.£9 

.49 

|3    x  2    x   i 

22.5 

1.92 

.67 

.47 

.92 

.55 

.46 

1*08 

.58 

150 

j3£  x  2£  x  -fa 

17.8 

2.19 

.94 

.56 

1.11 

.73 

.56 

1.14 

.64 

[8|  x  2j  x   £ 

27.5 

3.24 

1.86 

.87 

1.08 

.70 

.56 

1.20 

.70 

151 

6     x  3i  x  •& 

39.6 

14.76 

3.81 

2.68 

1.93 

.98 

.82 

2.06 

.81 

6    x  8i  x   1 

85.0 

29.24 

7.21 

5.75 

1.86 

.92 

.81 

2.26 

1.01 

152 

16^x4    xft 
6£  x  4    x    1 

44.0 
95.0 

19.29 
38.66 

5.723.87 
11.008.35 

2.(i9 

2.02 

1.14 
1.08 

.94 
.93 

2.18 
2.88 

.93 
1.18 

153 

5Jr   X   3£   X    f 

32.3  10.12 

3.2712.14 

1.77 

1.05 

.81 

1.82 

.82 

5|  x  3|  x   |   52.3 

15.73 

4.963.35 

1.73 

.97 

.80 

1.91 

.91 

154 

7     x  3|  x   |  01.7 

30.25 

5.284.45 

2.21 

.92 

.85 

2.57 

.82 

7    x  3£  x   l||95.0 

|45.37 

7.536.70 

2.19 

.88 

.84 

2.71 

.96 

155 

2£  x  2    x    i 

110  6 

.71 

.37 

.20 

.81 

.59 

.43 

.78 

.54 

2^  x  2    x    | 

20.0 

1.09 

.63 

.3? 

.74 

.56 

.43 

.87 

.62 

156 

2i  x  H  x  136 

6  7 

.34 

.13 

.08 

.71 

.43 

.34 

.76 

.38 

8i  x  li  x    2 

12.6 

.5( 

.21 

.15 

.63 

.40 

.34 

.82 

.44 

157 

2    x  1*  x  A 

5.7 

.23 

.07 

.05 

.63 

.35 

.31 

.68 

.31 

2    x  H  x    f 

9.2 

o. 

.10 

.08 

.59 

.33 

.29 

.70 

.32 

100 


WROUGHT  IKON  AND   STEEL. 
C 


ELEMENTS  OF 


A — x-B 


PENCOYD  TEES. 


EVEN   LEGS. 


I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

fc 

H 
O 

70 

SIZE  IN  INCHES. 

WEIGHT  PER 
YARD. 

MOMENTS  OF 
INERTIA. 

KADII  OF 
GYRATION. 

DISTANCE,  </, 
I"*"  FROM  BASE  TO 
^  NEUTRAL  Axis. 

Axis 
A.  B. 

Axis 
C.  D. 

Axis 
A.  B. 

Axis 
C.  D. 

4     x  4     x    £ 

36.5 

5.26 

2.55 

1.20 

.84 

71 

3£  x  3£  x  B 

31. 

3.47 

1.70 

1.06 

.74 

1.00 

72 

3    x  3    x  M 

26. 

2.10 

1.01 

.90 

.62 

.90 

73 

2*  x  2|-  x  -ft 

19.5 

1.12 

.58 

.78 

.55 

-.75 

74 

2J  x  2}  x    | 

17.52 

.97 

.49 

.75 

.53 

.75 

75 

21-  x  21  x   { 

11.75 

.52 

.30 

.65 

.50 

.61 

76 

21-  x  21  x  & 

12. 

.54 

.27 

.67 

.47 

.65 

77 

2    x  2    x  & 

10.5 

.38 

.19 

.60 

.43 

.60 

78 

If  x  If  x  & 

7.1 

.21 

.10 

.54 

.37 

.50 

79 

U  x  1*  x  A 

6. 

.13 

.06 

.46 

.32 

.45 

80 

n  x  11  x  v*. 

4.5 

.07 

.04 

.37 

.27 

.37 

81 

1     x  1     x  A 

3.0 

.03 

.02 

.30 

.26 

.30 

82 

3    x  3    x  M 

19.3 

1.59 

.75 

.91 

.62 

.84 

83 

8    x  8    x  if 

22.6 

1.83 

.89 

.90 

.63 

.86 

ELEMENTS   OF  PENCOYD  TEES. 
C 


101 


ELEMENTS 


UNEVEN   LEGS. 


TEES. 


I. 

II. 

III. 

IV. 

V. 

VI. 

VII. 

VIII. 

K 
M 
M 
i 

1 
0 

90 

SIZE  IN  INCHES. 

P 

44.5 

MOMENTS  OP 
INERTIA. 

RADII  OF 
GYRATION. 

fill 

Axis 
A.  B. 

Axis 
C.  D. 

Axis 
A.  B. 

Axis 
C.  D. 

4ix3i 

5.27 

3.66 

1.09 

.91 

1.16 

91 

4     x  3i 

41.8 

4.65 

3.23 

1.05 

.88 

1.09 

92 

5     x  2£ 

30.7 

1.61 

4.01 

.72 

1.14 

.67 

93 

5     x  2t 

33.0 

1.63 

4.58 

.70 

1.17 

.64 

94 

4x3 

25.9 

1.94 

2.18 

.86 

.92 

.77 

95 

4x3 

25.25 

2.09 

1.69 

.91 

.82 

.84 

96 

4x2 

20.4 

.68 

1  68 

.58 

.91 

.54 

97 

3     x  3| 

28.25 

3.12 

1.06 

1.05 

.61 

1.10 

98 

3     x  2£ 

23.8 

1.38 

.94 

.76 

.63 

.82 

99 

3     x  1^ 

11.2 

.19 

.56 

.41 

.71 

.37 

100 

at  x  H 

9.1 

.10 

.33 

.33 

.60 

.32 

101 

2     x  li 

8.75 

.16 

.18 

.43 

.45 

43 

102 

2x1 

7. 

.05 

.17 

.26 

.49 

.27 

103 

2     x  & 

5.88 

.01 

.17 

.13 

.54 

.17 

104 

2f  x  If 

18.75 

.56 

.62 

.55 

.58 

.66 

105 

21  x  2 

21. 

.83 

.63 

.63 

.55 

.75 

106 
107 

5     x  3t 
5x4 

48.44 
44.1 

5.37 
6.24 

5.31 
5.25 

1.05 
1.19 

1.04 
1.09 

1.05 
1.08 

108 

a±  x  -ft 

6.5 

.01 

.24 

.12 

.61 

.18 

109 

4x4^ 

38.5 

7.26 

2.70 

1.37 

.84 

1.32 

110 

3    x  2£ 

17.6 

.94 

.74 

.73 

.65 

.69 

111 

3    x  2t 

20.6 

1.08 

.so 

.72 

.66 

.70 

102  WROUGHT  IRON  AND   STEEL. 


MOMENTS  OF  INERTIA. 

The  following  formulae  were  used  in  calculating  the  moments 
of  inertia  and  radii  of  gyration  of  the  various  sections  given  in 
the  tables,  pages  93-101. 

When  not  otherwise  specified  the  axis  referred  to  passes 
through  the  centre  of  gravity  of  the  section,  in  a  horizontal 
position  to  the  figure  as  shown. 

I  signifies  moment  of  inertia. 
A       "        total  area  of  section. 
R       "        radius  of  gyration. 

d       "        distance  from  base  to  centre  of  gravity. 

In  all  cases  the  radius  of  gyration  =  JL/— ,  and  the  moment  of 

resistan     —  /  x  co-efficient  for  strength  of  material 

~~  distance  from  neutral  axis  to  farthest  edge  of  section* 


SOLID  RECTANGLE. 
T  _  bh3        Ak* 

=  13  =~12' 
r  /,  axis  xy  =  -^-- 

HOLLOW  RECTANGLE  OR  I  BEAM  WITH  PARALLEL  FLANGES. 
t 6 — ^.     f — 6—4 


-h        --'W-t-i- — /I          *  — 


MOMENTS    OF   INERTIA. 

SOLID   TRIANGLE. 


bh* 

/,  axis  xy  =  -—  - 

W*3 

J,  axis  uv  =  -H— 
o 


SOLID  CIRCLE. 


1=  . 


.<_Air 
:    16  ' 


HOLLOW  CIRCLE. 

/  =  (outer  radius 4  -  inner  radius 4)  .  7854 


SOLID  SEMICIRCLE. 

sjt*Z2±±:w   /.  axis  xy  =  .3927r4  = 
d  =  .4244r. 


SOLID  ELLIPSE. 


J=  . 


104 


WKOUGHT  IKON  AND   STEEL. 
TEE   SECTION. 


3 


„. 

~2A         '« 


•L  = 


ANGLE  SECTION. 

tc*  +  bd*  -(b-t)(d-  t)3 


For  even  or 


uneven  angles. 
/,  axis  *„  =  *(* 


6     N^/        For  uneven  angles. 
xy  passes  through  centre  of  gravity  parallel  to  ee. 

-(--4)7 


Foreven 


angles. 
A  close  approximation  for  the  latter  is  the  following  : 


I,  axis  xy  =  — — .    For  even  angles. 

^5 


/,  axis  xy  =  js  For  uneven  an 


,, 
»  = 


t(tf-t*)     ™ 
-JJ-T-    — -.    For  even  and  uneven  an- 

aJL 


„ 

.     For  uneven  angles. 


MOMENTS   OF    INERTIA. 


105 


In  even  angles  radius  of  gyration  around  xy  =  two-thirds  (f) 
of  the  radius  of  gyration  around  horizontal  axis. 

In  uneven  angles  the  distance  from  centre  of  gravity  in  direc- 
tion of  the  long  leg  exceeds  that  in  the  direction  of  the  short  leg 
by  half  the  difference  in  the  length  of  the  two  legs. 


I  BEAM   SECTION. 

8  =  taper  of  flange. 


cs* 


b  - 


*-^S*        J,axiS*y  =  -6-+i2.+  -~ 

b       t 


CHANNEL   SECTION. 

s  —  taper  of  flange. 


r  — 


l-t' 


1= 


12 

2mb3  +  If 


axis  xy  = 


d  = 


3 


106  WEOUGHT  IEON  AND   STEEL. 

DECK  BEAM   SECTION. 

*  =  taper  of  flange.  a  =  area  of  bulb. 


o  =  m  —  -  . 
3 


86 

nf 


a  (2  h  -  £)  +  t  (h  -  k'f  +  (b  -  t)  p*+  s(l-t)  (p  +  - 


In  the  table  of  elements,  pages  92-101,  the  moments  of  inertia 
and  radii  of  gyration  are  given  for  the  minimum  section  of  each 
shape  but  the  moment  of  inertia,  for  any  increased  section  can 
readily  be  ascertained  as  follows,  without  recalculating  the 
whole. 

FOB  ANY  I  BEAM,  CHANNEL  BAR  OR  DECK  BEAM. 

AXIS  PERPENDICULAR  TO  WEB. 

Let  a  =  increase  of  area  in  square  inches  over  minimum  sec- 
tion given  in  the  table.  Let  d  —  depth  (size)  of  beam,  then 

—  is  the  moment  of  inertia  for  increase  of  area,  which  added  to 

1,0 

tabular  figures  gives  the  correct  result  for  the  enlarged  section. 
Example. — A  12"  I  Beam,  No.  4,  area  12  square  inches,  is  in- 

O      y      1  O2 

creased  to  14  square  inches.      - — ^-  =  24,  which  added  to  the 

moment  given  in  col.  7—272.86  +  24  =  296.86,  the  moment  of 
inertia  desired. 


MOMENTS   OF  INERTIA.  107 

/272  8fi 

Radius  of  gyration  of  the  former  A/  =4.78  inches. 

'        12 

A>Qfi   ftfi 

Radius  of  gyration  of  the  latter  y  ^°-go  =4.60  inches. 

The  radius  of  gyration  will  be  found  to  alter  very  little,  and 
for  all  practical  purposes,  the  tabular  figures  may  be  accepted 
within  the  range  of  section  possible  for  each  shape. 

The  above  is  only  a  close  approximation  for  deck  beams. 

FOR  ANY  I  BEAM  OR  DECK  BEAM. 

AXIS   PARALLEL   WITH  WEB. 

The  following  rule  gives  a  close  approximation  for  the  mo- 
ment of  inertia. 

Multiply  the  increase  of  area  in  square  inches  by  the  total 
thickness  of  web  in  the  enlarged  section.  This  product  added 
to  the  tabular  number  in  col.  8,  will  give  the  moment  of  inertia 
for  the  enlarged  section. 

Example. — A  10"  I  Beam,  No.  8,  area  9  square  inches  is  in- 
creased to  10f  square  inches,  having  a  web  thickness  of  .525 
inches.  .  525  x  l£  =  .  7875,  which  added  to  the  amount  in  col. 
VIII.,  8.09  +  .78  =  8.87,  the  moment  of  inertia  required. 

Radius  of  gyration  of  least  section  =  A/  _ —  = .  95  inches. 

f       9 

Radius  of  gyration  of  enlarged  section  =  4/         =.92  inches. 

'     10.5 

The  radius  of  gyration  alters  but  very  little,  and  may  be  ac- 
cepted as  practically  unchanged  within  the  limits  that  any  shape 
can  be  increased. 

CHANNELS. 

For  channels,  in  relation  to  axis  parallel  to  web  the  moment 
of  inertia  increases  nearly  in  a  direct  ratio  to  the  increase  of 
sectional  area,  but  not  precisely  so,  this  ratio  being  too  great  for 
the  larger  sections  and  too  little  for  the  smaller  sizes  of  channel 
bars. 

The  radius  of  gyration  alters  but  little  as  the  sectional  area  is 


108  WKOUGHT   IKON   AND   STEEL. 

changed,  and  practically  may  be  accepted  as  unchanged  within 
the  range  of  variation  possible  for  any  particular  size. 

The  distance  d  will  not  vary  sufficiently  in  any  section  be- 
tween the  limits  of  minimum  and  maximum  to  make  any  prac- 
tical difference  in  ordinary  calculations  where  it  may  be  used. 

ANGLES. 

For  angles  referring  to  any  axis  passing  through  the  centre  of 
gravity,  the  inertia  increases  nearly  in  the  same  ratio  as  the  area 
increases.  Our  table  gives  values  of  /  for  the  minimum  and 
maximum  sections  ;  any  intermediate  section  can  be  obtained  by 
proportion  unless  great  accuracy  is  required.  Our  tables  ex- 
hibit the  change  in  values  of  R  between  the  least  and  greatest 
sections,  which  in  the  case  of  small  angles  remain  practically 
unaltered  within  the  range  of  possible  variation  of  area. 

INERTIA   OF    COMPOUND   SHAPES. 

"  The  moment  of  inertia  of  any  section  about  any  axis  is  equal 
to  the  /about  a  parallel  axis  passing  through  its  centre  of  grav- 
ity +  the  area  of  the  section  multiplied  by  the  square  of  the 
distance  between  the  axes." 

By  use  of  this  rule  the  moments  of  inertia  or  radii  of  gyration 
of  any  single  sections  being  known,  corresponding  values  can 
readily  be  obtained  for  any  combination  of  these  sections. 

TV^js  i 

i.i-\-T msia  Example  No.  1. — A  combination  of  two  9" 
54  Ib.  Channels,  and  two  12  x  {  plates  as 
shown. 


fc    ;/    I  >H  AXIS  A  B  OF  SECTION. 

/forB2  channels,  col.  VII,  page  94,  =  128.680 

/  for  2  plates  =  i?_^  i?2!  x  2  =        .  03125 ) 

r 
6  (area  of  plates)  x  4f  a  =  128 . 34375 )  =  128 . 375 

/for  combined  section  =  257.055 

which  divided  by  area  (14)  gives  18.3611  -  R2  or  4.285  radius  of 
combined  section. 


MOMENTS  OF  INERTIA.  109 

AXIS  C  D. 

Find  distance  d  =  (.67)  from  col.  XV.,  page  95,  then  obtaining 
the  distance  (4.2325)  between  axes  CD  and  EF. 

/for  2  channels  around  axis  JZFfrom  col.  VIII.,          =    4.94 
Area  of  channels  x  square  of  distance  =  10.8  x  4.2325'  =  193.471 

/ for  2  plates  ='5*123  =    72. 


/  for  combined  section  —  270 . 41 1 


Radius  of  gyration  =  j/270'411  =4.395. 


By  similar  methods,  inertia  or  radius  of  gyration  for  any  com- 
bination of  shapes  can  readily  be  obtained. 

Example  No.  2. — A  "  built-up  beam  "  composed  of  : 

~~>!l"  4  angles  3"  x  3"  x  \". 

2  plates  8"  x  |". 
1  plate  15"  x  F. 

AXIS   A  B. 

/of  two  8"  x  |  plates  =  9  *  ^  x  2  =      .167 

+  8  (area)  x  7f  (sq.  of  distance  d)  =480.5 

480.667 

/of  one  15"  x  |"  plate  =  ^^=  105.469 

/of  four  3  x  3  x  i  angles  =  4  x  1 .24  (see  col.  \ 

IV,  page  98),  =     4.96   }• 

+  5.7"  (area)  x  6.662  (sq.  of  distance  d1)  =255.045* 

260.005 


Inertia  of  combined  section  around  A  B  =  846  .  141 

846.141 


_    ,.  ..  7846.141 

Radius  of  gyration  =|/  -jg-g-^  =     6- 


61- 


110  WROUGHT  IRON  AND   STEEL. 

AXIS   C.  D. 

lot  two  8  x  \  plates  =^jj^  x  2  =  42.667 

I  of  one  15  x  |  plate  =  ^^-          =  .066 

La 

lot  four  3  x  3  x  £  angles  =  4  x  1.24  (see 


col.  IV,  page  98) 
+  5  .  75  (area)  x  1  .  02752  (sq.  of  distance  d") 

-    11.031 


ee  \ 

=    4.96  t 
d"      =    6  .  071  ) 


Inertia  of  combined  section  around  C  D  =    53 . 764 


Radius  of  gyration  =  V53-764  =     1 . 66. 
'    19 . 375 

RADIUS  OF  GYRATION  OF  COMPOUND   SHAPES. 

In  the  case  of  a  pair  of  any  shape  without  a  web  the  value  of 
It  can  always  be  readily  found  without  considering  the  moment 
of  inertia. 

The  radius  of  gyration  for  any  section  around  an  axis  parallel 
to  another  axis  passing  through  its  centre  of  gravity,  is  found 
as  follows  : 

Let  r  =  radius  of  gyration  around  axis  through  centre  of  grav- 
ity. R  —  radius  of  gyration  around  another  axis  parallel  to 
above,  d  —  distance  between  axes. 


"When  r  is  small,  R  may  be  taken  as  equal  to  d  without  mate- 
rial error.  Thus  in  the  case  of  a  pair  of  channels  latticed  to- 
gether, or  a  similar  construction. 

Example  No.  1. — Two  9"  54  Ib.  channels  placed  4.66"  apart, 
E  E  required  the  radius  of  gyration  around  axis  CD 
l-j— ^  for  combined  section. 

Find  r  on  col.  X.,  page  95,  =  .68  and  r2  =  .4624. 
Find  distance  from  base  of  channel  to  neutral  axis 
col.  XV.,  same  page,  =  .07,  this  added  to  \  distance 
between  the  two  bars,  2.33"=  3"  =  d,  and  d*  —  9. 
Radius  of  gyration  of  the  pair  as  placed  equals, 


MOMENTS  OF  INEETIA.  Ill 


The  value  of  J?  for  the  whole  section  in  relation  to  the  axis  A 
B  is  the  same  as  for  the  single  channel,  to  be  found  in  the 
tables. 

Example  No  2.  —  Four  3"  x  3"  x  f"  angles  placed  as  shown; 
form  a  column  10  inches  square;  required  the 
i8y,radius  of  gyration. 

Find  T  OQ  C0i>  VI)  Page  98'  =  -91'  atld  ?'2  ~ 

-8281. 

Find  distance  from  side  of  angle  to  neutral 
P|  f\     axis,  coi.  VII.  ,  same  page,  =  .  89.  Subtract  this 

I  i  _  t  j  |     from  |  the  width  of  column  =5.  —  .89  = 

p  4.11  =  d  or  distance  between  two  axes,     d2  = 

16.8921. 
Radius  of  gyration  of  4  angles  as  placed  = 


-i*"3""!  I?*  s  _  i8 

I'M 
IJi11 


•  _ 


-Y/16.8921  +  .8281  =4.21. 

When  the  angles  are  large  as  compared  with  the  outer  dimen- 
sions of  the  combined  section,  the  radius  of  gyration  can  be 
taken  without  serious  error  from  the  table  of  radii  of  gyration 
for  square  columns,  on  page  155. 


112 


WROUGHT  IRON  AND   STEEL. 


O    O    Q 

sil 

i 

fc    §    ^ 

M 

*                    * 

"*^         -i 

h 

ill 

o 

§ 

• 
g 

r§                                                                     S                                                                      -§ 

g|  g 

0    ^S 
5   |* 

s 
a 

|*                                                         j§                                                                      « 

1 

•""v  •  ' 

^aS 

s 

^  II 

RATION. 

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RADIUS  OF  GYRATION. 


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WROUGHT  IRON  AND   STEEL. 


ROLLED  IRON  STRUTS. 

In  the  following  consideration  of  rolled  struts  of  various 
shapes,  the  least  radius  of  gyration  of  the  cross  section  taken 
around  an  axis  through  the  centre  of  gravity  is  assumed  as  the 
effective  radius  of  the  strut.  The  resistance  of  any  section  per 
unit  of  area  will  in  general  terms  vary  directly  as  the  square  of 
the  least  radius  of  gyration,  and  inversely  as  the  square  of  the 
length  of  the  strut.*  The  shape  of  the  section  and  the  distribu- 
tion of  the  metal  to  resist  local  crippling  strains  must  also  be 
considered.  As  a  rule,  that  shape  will  be  strongest  which  pre- 
sents the  least  extent  of  flat  unbraced  surface.  For  instance, 
two  M  sections  of  unequal  web  widths  may  have  the  same  web 
thickness,  the  same  flange  area,  and  the  same  least  radius  of  gy- 
ration, but  the  wider  webbed  section  will  be  the  weaker  per  unit 
of  area,  on  account  of  the  greater  extent  of  unbraced  web  sur- 
face it  contains.  For  the  same  reason  a  hollow  rectangular  sec- 
tion, composed  of  thin  plates  will  be  to  some  extent  weaker  than 
a  circular  section  of  the  same  length  having  the  same  arta  and 
radius  of  gyration. 

END  CONNECTIONS. 

As  is  well  known,  the  method  of  securing  the  ends  of  the  struts 
exercises  an  important  influence  on  their  resistance  to  bending, 
as  the  member  is  held  more  or  less  rigidly  in  the  direct  line  of 
thrust. 

In  the  tables,  struts  are  classified  in  four  divisions,  viz. : 
"  Fixed  Ended,"  "Flat  Ended,"  "  Hinged  Ended,"  and  "  Round 
Ended." 

In  the  class  of  "  fixed  ends"  the  struts  are  supposed  to  be  so 
rigidly  attached  at  both  ends  to  the  contiguous  parts  of  the 
structure  that  the  attachment  would  not  be  severed  if  the  mem- 
ber was  subjected  to  the  ultimate  load.  "Flat  ended  "  struts 
are  supposed  to  have  their  ends  flat  and  square  with  the  axis  of 
length  but  not  rigidly  attached  to  the  adjoining  parts.  "  Hinged 

*  This  applies  only  to  long  struts  with  free  euds. 


ROLLED  IRON  STRUTS.  115 

ends  "  embrace  the  class  which  have  both  ends  properly  fitted 
with  pins,  or  ball  and  socket  joints,  of  substantial  dimensions  as 
compared  with  the  section  of  the  strut ;  the  centres  of  these  end 
joints  being  practically  coincident  with  an  axis  passing  through 
the  centre  of  gravity  of  the  section  of  the  strut.  "  Round 
ended  "  struts  are  those  which  have  only  central  points  of  con- 
tact, such  as  balls  or  pins  resting  on  flat  plates,  but  still  the  cen- 
tres of  the  balls  or  pins  coincident  with  the  proper  axis  of  the 
strut. 

If  in  hinged-euded  struts  the  balls  or  pins  are  of  comparatively 
insignificant  diameter,  it  will  be  safest  in  such  cases  to  consider 
the  struts  as  round  ended. 

If  there  should  be  any  serious  deviation  of  the  centres  of  round 
or  hinged  ends  from  the  proper  axis  of  the  strut,  there  will  fee  a 
reduction  of  resistance  that  cannot  be  estimated  without  know- 
ing the  exact  conditions.  No  formula  has  been  written  which 
expresses  with  accuracy  the  resistance  to  compression  for  various 
sections  and  for  an  extended  range  of  lengths.  It  is  doubtful  if 
any  simple  formula  admitting  of  ready  practical  application  can 
be  devised;  in  fact  none  is  required,  as  the  results  of  experiments 
can  be  embodied  in  tables  and  diagrams  in  such  a  compact  form 
that  their  application  to  any  length  or  section  can  be  readily 
made. 

When  the  pins  of  hinged-end  struts  are  of  substantial  diam- 
eter, well  fitted,  and  exactly  centred,  experiment  shows  that  the 
hinged  ended  will  be  equally  as  strong  as  flat  ended  struts. 

But  a  very  slight  inaccuracy  of  the  centring  rapidly  reduces 
the  resistance  to  lateral  bending,  and  as  it  is  almost  impossible 
in  practice  to  uniformly  maintain  the  rigid  accuracy  required, 
it  is  considered  best  to  allow  for  such  inaccuracies  to  the  extent 
given  in  the  tables,  which  are  the  average  of  many  experi- 
ments. 

TABLES  OF   STRUTS. 

In  table  No.  1,  the  first  column  gives  the  effective  length  of 
the  strut  divided  by  the  least  radius  of  gyration  of  its  cross  sec- 
tion, and  the  successive  columns  give  the  ultimate  load  per 
square  inch  of  sectional  area  for  each  of  the  four  classes  afore- 


116  WROUGHT  IRON  AND  STEEL. 

said.  We  mean  by  "  ultimate  load  "  that  pressure  under  which 
the  strut  fails. 

These  ultimate  loads  are  the  averages  of  a  number  of  experi- 
ments which  we  have  recently  made  on  carefully  prepared  spec- 
imens, and  are  believed  to  be  trustworthy. 

For  hinged-ended  struts  the  figures  apply  to  those  cases  in 
which  the  axis  of  the  pin  is  at  right  angles  to  the  least  radius  of 
gyration,  or  in  which  the  strut  is  free  to  rotate  on  the  pin  in  its 
weakest  direction.  If  the  pin  should  be  placed  in  another  direc- 
tion, or  if  the  strut  should  be  secured  from  failure  in  its  weakest 
direction,  there  will  be  a  correction  for  determining  the  resist- 
ance as  hereafter  described. 

FACTORS   OF   SAFETY. 

It  is  considered  good  practice  to  increase  the  factors  of  safety 
as  the  length  of  the  strut  is  increased,  owing  to  the  greater  in- 
ability of  the  long  struts  to  resist  cross  strains,  etc.  For  similar 
reasons  we  consider  it  advisable  to  increase  the  factor  of  safety 
for  hinged  and  round  ends  in  a  greater  ratio  than  for  fixed  or 
flat  ends. 

Presuming  that  one-third  of  the  ultimate  load  would  consti- 
tute the  greatest  safe  load  for  the  shortest  struts,  the  following 
progressive  factors  of  safety  are  adopted  for  the  increasing 
lengths. 

3.  +  .01  —  for  flat  and  fixed  ends. 
r 

3  +  .015  — for  hinged  and  round  ends. 
r 

I  =  length  of  strut. 
r  —  least  radius  of  gyration. 
From  the  above  we  derive  the  following  table  : 


EOLLED   IKON  STRUTS. 


117 


FACTORS  OF  SAFETY. 


R  * 

P  r\ 

Pa 

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20 

3.2 

3.3 

150 

4.5 

5.25 

280 

5.8 

7.2 

30 

3.3 

3.45 

160 

4.6 

5.4 

290 

5.9 

7.35 

40 

3.4 

3.6 

170 

4.7 

5.55 

300 

6.0 

7.5 

50 

3.5 

3.75 

180 

4.8 

5.7 

310 

6.1 

7.65 

60 

3.6 

3.9 

190 

4.9 

5.85 

320 

6.2 

7.8 

70 

3.7 

4.05 

200 

5.0 

6.0 

830 

(5.3 

7.95 

80 

3.8 

4.2 

210 

5.1 

6.15 

340 

6.4 

8.1 

90 

3.9 

4.35 

220 

5.2 

6.3 

350 

6.5 

8.25 

100 

4.0 

4.5 

2:50 

5.3 

6.45 

360 

6.6 

8.4 

110 

4.1 

4.65 

240 

5.4 

6.6 

370 

6.7 

8.55 

120 

4.2 

4.8 

250 

5.5 

6.75 

880 

6.8 

8.7: 

130 

4.3 

4.95 

260 

5.6 

6.9 

390 

6.9 

8.85 

140 

4.4 

5.1 

270 

5.7 

7.05 

400 

7.0 

9.0 

Table  No.  2  represents  the  greatest  safe  load  per  square  inch 
of  section  for  each  of  the  four  classes  of  struts  and  is  derived 
from  the  results  in  Table  No.  1  by  means  of  the  foregoing  fac- 
tors of  safety. 

The  remarks  on  page  33  for  safe  loads  on  beams,  apply  also  to 
struts.  The  loads  in  Table  No.  2  ought  to  be  applied  only 
under  the  most  favorable  circumstances,  such  as  an  invariable 
condition  of  the  load,  little  or  no  vibration,  etc.  Under  cer- 
tain conditions,  such  as  for  buildings,  bridges,  etc.,  the  least 
factor  of  safety  ought  to  be  four  (4),  which  would  increase  each 
factor  in  the  above  table  by  unity.  The  safe  load  will  then  be 
found  by  dividing  the  results  given  in  Table  No.  1  by  the  cor- 
rected factor  of  safety. 


118  WROUGHT  IEON  AND   STEEL. 

No.  1. 
WROUGHT  IRON  STRUTS. 

ULTIMATE   PRESSURE   IN  LBS.    PER   SQUARE  INCH. 


LENGTH 

FLAT 

FIXED 

HINGED 

ROUND 

LEAST     RADIUS 
OF  GYRATION. 

ENDS. 

ENDS. 

ENDS. 

ENDS. 

20 

46.000 

46,000 

46,000 

44,000 

80 

43,000 

43,000- 

43,000 

40,250 

40 

40.000 

40,000 

40,000 

36,500 

50 

3H,000 

38.000 

38,000 

33,500 

60 

36,000 

36,000 

3o,UOO 

3a,5>0 

70 

34,000 

34,000 

33,750 

27,750 

80 

32,000 

3-2,000 

31,500 

25,000 

90 

30,900 

31.000 

29,750 

22,750 

100 

29,800 

30,000 

28,000 

20.500 

110 

23,050 

29,000 

26,150 

18,500 

120 

26,300 

28,000 

24.300 

16500 

130 

24.900 

26,750 

22,650 

14.G50 

140 

23,500 

25,500 

21,000 

12,800 

150 

21,750 

24,250 

18,750 

11,150 

160 

20,000 

23,000 

16,500 

9,5  0 

170 

18,4:  K) 

21,500 

14,650 

8,500 

180 

16,800 

20,000 

12,800 

7,500 

190 

15.650 

18,750 

11,800 

6.750 

200 

14.500 

17,500 

10.800 

6,000 

210 

13,600 

16.250 

9.800 

5,500 

220 

12,700 

15,000 

8.800 

s.noo 

230 

11,950 

14,000 

8.150 

4,650 

240 

11,200 

13,000 

7.500 

4,300 

250 

10,500 

12,000 

7,000 

4,050 

260 

9,800 

11,000 

6,500 

3,800 

270 

9,150 

10,500 

6.100 

3.500 

280 

8,500 

10,000 

5,700 

3,200 

290 

7,850 

9,500 

5.350 

3,01)0 

300 

7,200 

9000 

5.000 

2.800 

310 

6,600 

8,500 

4,750 

2.650 

320 

6,000 

8.000 

4,500 

2,500 

330 

5,550 

7,500 

4,2.50 

2,300 

340 

5,100 

7,000 

4,000 

2.100 

350 

4,700 

6,750 

3.750 

2,000 

360 

4,300 

6,500 

3500 

1,900 

370 

3.900 

6.150 

3.250 

1,800 

380 

3.500 

5.800 

3,000 

1,700 

390 

3,250 

6,800 

2,750 

1,600 

400 

3,000 

5,200 

2.500 

1,500 

410 

2750 

5,0(10 

2,400 

1,400 

420 

2.500 

4.800 

2.300 

1,300 

430 

2,.350 

4.550 

2.200 

440 

2,200 

4.300 

2,100 

450 

2,100 

4,050 

2,000 

460 

2,000 

3,8CO 

1,900 

470 

1,950 

1,850 

480 

1,900 

1,800 

WROUGHT   IRON   STEUTS. 


119 


No.  2. 
GREATEST  SAFE  LOADS  ON  STRUTS. 

Greatest  safe  load  in  Ibs.  per  square  inch  of  cross  section  *or  vertical  struts. 
Both  ends  are  supposed  to  be  secured  as  indicated  at  the  head  of  each  col- 
umi?..  If  both  ends  are  not  secured  alike,  take  a  mean  proportional  between 
the  values  given  for  the  classes  to  which  each  end  belongs.  If  the  strut  is 
hinged  by  any  uncertain  method  so  that  the  centres  of  pins  and  axis  of  strut 
may  not  coincide,  or  the  pins  may  be  relatively  small  and  loosely  fitted,  it  is 
best  in  such  cases  to  consider  the  strut  as  "  round  ended." 


LENGTH 

FLAT 

FIXED 

HINGED 

ROUND 

LEAST   RADIUS 
OP  GYRATION. 

ENDS. 

ENDS. 

ENDS. 

ENDS. 

20 

30 

14,380 
13,030 

14.380 
13,'  30 

13,940 
12,460 

13,330 
11,670 

40 

11,760 

11,760 

11.110 

10.140 

50 

10,860 

10,860 

10,130 

8,930 

60 

10,000 

10,000 

9,230 

7,820 

70 

9,190 

9.190 

8,330 

6,850 

80 

8,420 

8,420 

7,500 

5,950 

90 

7,920 

7,950 

6,840 

5,230 

100 

7,450 

7,500 

6,220 

4,560 

110 

6,840 

7.070 

5.620 

3,980 

.    120 

6,260 

6,670 

5.060 

3,440 

130 

5,  '.90 

6,220 

4.580 

2,960 

140 

5,340 

5,800 

4,120 

2,510 

150 

4,830 

5,390 

3.570 

2,120 

160 

4,350 

5,000 

3,060 

1,760 

170 

3,920 

4,570 

2,640 

1,530 

180 

3,500 

4.170 

2,250 

1,310 

190 

3,190 

3,830 

2,020 

1,150 

200 

2,900 

3,500 

1,800 

1,000 

210 

2,<;70 

3,190 

1,590 

890 

220 

2,440 

2.880 

1,400 

790 

230 

2,250 

2.G40 

1,260 

720 

240 

2,070 

2,410 

1,140 

650 

250 

,910 

2,180 

1,040 

600 

260 

,750 

1.960 

940 

550 

270 

,610 

1,S40 

870 

500 

280 

,460 

1,720 

790 

440 

290 

,330 

1,610 

730 

410 

300 

1,200 

1,500 

670 

370 

310 

,080 

1,390 

620 

350 

320 

970 

1,290 

580 

320 

830 

880 

1,190 

540 

290 

340 

800 

IJ'90 

490 

260 

350 

720 

1,040 

450 

240 

360 

650 

980 

420 

230 

370 

580 

920 

380 

210 

380 

510 

850 

340 

200 

890 

470 

800 

310 

80 

400 

430 

740 

280 

70 

120         WKOUGHT  IRON  AND  STEEL. 

ROLLED  STRUCTURAL  SHAPES  AS  STRUTS. 

The  following  tables  for  the  working  values  of  various  rolled 
structural  shapes  as  struts  are  derived  directly  from  Table  No. 
2.  The  radii  of  gyration  are  taken  from  Tables  of  Elements, 
pages  92-101.  In  all  cases  the  strut  is  supposed  to  stand  verti- 
cal. In  short  struts  this  distinction  is  immaterial,  but  when  the 
length  becomes  considerable,  the  deflection  resulting  from  its 
own  weight,  if  horizontal,  would  seriously  affect  the  stability  of 
the  strut. 

The  tables  are  calculated  for  the  minimum  section  of  each 
shape.  For  sections  increased  above  the  minimum  the  resist- 
ance per  square  inch  will  dimmish.  This  amount  can  be  accu- 
rately determined  by  finding  the  correct  radius  of  gyration  for 
the  enlarged  section  as  heretofore  described.  But  within  the 
range  of  variation  of  section  possible  for  any  shape,  the  tables 
may  be  accepted  as  practically  correct.  The  head  notes  to  the- 
tables  indicate  the  condition  assumed  for  each  class  of  Ft  ruts. 
If  the  pins  should  be  placed  otherwise  than  as  described  in  the 
tables,  the  strut  may  be  either  weaker  or  stronger,  according  to 
circumstances,  which  have  to  be  determined  for  any  particular 
case.  This  results  from  the  fact  that  a  pin-connected  strut  if 
properly  designed  should  be  considered  hinged  ended,  only  in 
the  direction  in  which  it  is  free  to  rotate  on  the  pin. 

'In  the  direction  of  the  axis  of  the  pin  it  can  be  treat  ed  as  a 
"  flat  ended  "  strut.  An  I  beam  strut  of  the  character  described 
in  Tables  3,  4,  and  5,  braced  laterally  in  the  direction  of  its 
flanges  should  be  considered  also  by  Tables  6,  7,  and  8,  as  a 
series  of  short  struts  whose  lengths,  are  the  distances  between 
points  of  bracing,  and  liable  to  fail  in  the  direction  of  the 
flanges. 

Example.— An  8"  65  Ib.  I  beam,  18  feet  long  is  used  as  a  strut 
having  pins  at  both  ends  at  right  angles  to  web.  It  would  then 
be  flat  ended  in  the  direction  of  the-  flanges,  and  by  Table  No. 
7  the  greatest  safe  load  —  1,990  Ibs.  per  square  inch  of  section. 
If  braced  in  the  direction  of  the  flanges  at  two  points  6  feet 
apart  it  should  then  be  considered  as  a  series  of  flat  ended  struts 
C  feet  long,  whose  safe  load  by  Table  No.  7,  would  be  8,320  Ibs. 
per  square  inch. 


CHANNEL  STRUTS.  121 

In  the  direction  of  its  web  it  remains  a  hinged-ended  strut  18 
feet  long,  and  safe  load  by  Table  No.  4  —  8,690  Ibs.  per  square 
inch. 

CHANNEL  STRUTS. 

The  foregoing  remarks  apply  also  to  channels,  which  are  seldom 
used  individually  as  struts,  but  frequently  in  pairs.  When  so 
used,  if  the  methods  of  connection  are  not  of  such  a  nature  as  to 
insure  the  unity  of  action  of  the  pair,  they  should  be  treated  as 
an  assemblage  of  separate  struts .  But  if  connected  by  a  proper 
system  of  triangular  latticing,  the  pair  can  be  considered  as  a 
unit,  and  each  channel  treated  as  a  series  of  short  struts  whose 
length  is  the  distance  between  centres  of  latticing. 

Example. — A  pair  of  9"  54  Ib.  channels,  separated,  etc.,  as 
described  on  page  110,  are  connected  by  triangular  latticing, 
forming  a  hinged-ended  strut  10  feet  between  pin  centres.  WLat 
is  the  greatest  safe  load,  and  how  far  can  latticing  be  spaced  ? 

As  described  on  page  95,  radius  of  gyration  around  axis  across 
the  web  of  channel,  or  in  the  direction  of  the  pin  =  3 . 45  inches. 
Eadius  of  gyration  in  opposite  direction  =  3.07  inches.  Least 
radius  of  gyration  for  a  single  channel  =  .  68  inch. 

—  for  hinged-ended  direction  =  35,  and  by  Table  No.  2  Safe 

Load =11, 800  Ibs.    —  for  flat-ended  direction  =  39,  and  by  same 
T 

table  greatest  safe  load  =  11,900  Ibs. 

For  each  single  channel  the  greatest  length  between  latticing 
=  radius  of  gyration  x  39  =  26|  inches. 

It  is  customary  and  is  also  good  practice  to  reduce  the  dis- 
tance between  lattice  centres  below  v'liat  the  above  calculation 
would  require. 

Tables  Nos.  12-14,  give  the  greatest  safe  loads  per  square 
inch  of  sectional  areas,  for  struts  composed  of  a  pair  of  channels 
properly  connected  together,  so  as  to  insure  unity  of  action.  The 
figures  are  derived  from  Table  No .  2. 

The  distances  D  or  d,  for  channels  placed  flanges  inward  or 
flanges  outward  respectively,  make  the  radii  of  gyration  equal 
lor  either  direction  of  axis. 

These  distances  should  not  be  diminished,  and  may  be  ad  van- 


122 


WROUGHT  IRON  AND   STEEL. 


tageously  increased,  especially  for  hihged-ended  struts,  if  the  pin 
is  placed  parallel  to  the  webs  of  the  channels.  These  tables  are 
calculated  for  the  standard  minimum  section  of  each  channel. 
The  distance  d  may  be  slightly  diminished  for  sections  heavier 
than  the  minimum,  but  the  diminution  can  be  so  little  that  it  is 
practically  unnecessary  to  notice  it.  Under  each  length  of  struts 
in  the  table  I  represents  the  greatest  distance  apart  in  feet  that 
centres  of  lateral  bracing  can  be  spaced,  without  allowing  weak- 
ness in  the  individual  channels.  The  distance  I  is  obtained  as 

shown  in  last  example,  that  is,  by  making  —  =  —  • 

T  Mi 

I  =  length  between  bracing. 
L  =  total  length  of  strut. 

T  =  least  radius  of  gyration  for  a  single  channel. 
JB  =  least  radius  of  gyration  for  the  whole  section. 


STEEL  STKUTS.  123 


STEEL  STRUTS. 

A  table  for  the  ultimate  resistance  of  flat-ended  struts  of  two 
grades  of  steel  will  be  found  on  page  31.  These  grades  prob- 
ably embrace  the  extremes  of  the  material,  that  is,  the  hardest 
and  softest  steels  that  are  likely  to  be  used  in  struts. 

Experiments  on  this  material  are  not  sufficiently  complete  to 
warrant  a  full  statement  of  resistances  of  the  various  grades, 
and  for  the  various  conditions  of  the  strut,  such  as  the  methods 
of  connecting  the  ends,  etc. 

It  is  probable,  however,  that  the  relations  existing  between 
the  four  classes  of  wrought-iron  struts,  as  given  in  the  following 
tables,  will  also  prevail  in  the  same  ratios  for  steel.  The  safe 
loads  for  steel  struts  of  any  section  or  length,  can  therefore  be 
obtained  by  increasing  the  figures  in  the  following  tables,  for 

any  ratio  of  — ,  in  the  proportions  given  on  page  81,  as  existing 
T 

between  flat-ended  struts  of  iron  and  steel. 

When  a  grade  of  steel  is  used,  intermediate  in  hardness  be- 
tween the  mild  and  hard  heretofore  described,  it  is  probable  that 
the  strut  resistance  for  such  material  may  be  safely  approxi- 
mated by  simple  proportion. 

For  instance,  the  steels  referred  to  had  carbon  ratios  of  .  12 
and  .38  per  cent,  respectively.  A  mean  proportion  of  these 
would  be  .24  per  cent. 

It  is  probable  that  steel  of  latter  grade  would  possess  inter- 
mediate compressive  resistance  between  the  two  grades  described 
from  our  experiments. 


124:  WROUGHT  IKON  AND   STEEL. 

No.  3. 

PENCOYD  I  BEAMS  AS  STRUTS. 

GREATEST   SAFE   LOAD  IN  LBS.    PER   SQUARE  INCH   OF   SECTION. 

When  the  struts  are  secure  from  failure  in  the  direction  of  the  flanges,  and 
can  bend  only  in  the  direction  of  the  web  C  D.  Using  factors  of  safety 
given  in  previous  tables. 


SIZE 

CONDITION 

LENGTH  IN  FEET. 

BEAM. 

OP 

8 

10 

12 

14 

16 

18 

20 

22 

24 

IK" 

Fixed  Ends..  . 

14240 

13700 

13160 

1-2650 

12140 

11670 

11310 

10950 

L  U 

Flat  Ends  

14240  13700  13160  12650  12140 

11670!!  1310 

10950 

Heavy  

Hinged  Ends... 

137901  13200!  12610!  12050  11510 

11010,10620 

10230 

I  i=  5  •  Htt 

Round  Ends 

13160  12500  11840  11210  10600 

10020    9530 

9050 

;, 

Fixed  Ends  

14380 

13840 

13300 

1278:) 

12270 

11760 

11400 

11040 

-L  t/ 

Flat  Ends 

14380  1384  l  13300  12780  12270 

11760  11403 

11040 

Light6_. 

Hinged  Ends... 

13940  13350  12760  1  '21  90  1  1650 

1111010720 

10330 

Round  Ends. 

13*30 

12670  12000  11360  10750  101401  9660 

9170 

1  9" 

Fixed  Ends  

| 

14380J13570 

12900 

12270 

11670 

11220 

10770 

10340 

9920 

L  _j 

Heavy  

Flat  Ends  
Hinged  Ends... 

1438013570 
13940  i  13050 

12900  12270  11670  11220  10770  10:340 
123201  1  1  650  !  1  1010  10520  10040    9590 

9920 
9140 

r  =  4-69 

Round  Ends  

13330 

12330 

11520 

10750 

10020 

9410   8820 

8260 

7720 

1  9" 

Fixed  Ends.... 

14380 

13700 

13030 

12400 

11760 

11310'  10860 

10430 

10000 

JL  — 

Flat  Ends  

14880 

13700  13030  12400,  11760  11310  108<>0  10430 

10000 

Light       , 

HiMgedEnds... 

13940 

13200  12460111780  11110  106-20  10130 

9680 

9230 

I  —  4-7S 

Round  Ends  

13330 

12500 

116rt) 

10900 

10140 

9530 

8930 

8370 

7820 

-mi" 

Fixed  Ends.   . 

13970 

13160 

12400 

11760 

11220 

10690 

10170 

9760 

9270 

-L  U  n" 

Plat  Ends  

139  ;0 

1316012400 

11760 

1  1220  10690J  10170 

9760 

9270 

Heavy.... 

Hinged  Ends.  .  . 

13500 

1261011780 

11110 

10520    9950 

9410 

8960 

8420 

r  =  4«34 

Round  Ends  

12830 

11840 

10900 

10140 

9410    8710 

8040 

7530 

6950 

ioy 

Fixed  Ends... 
Flat  Ends  

13970 
13970 

13160 

13160 

12400 
12400 

11760 

1  1760 

11220(10690 
1122010690 

10170'  9760 
10170    9760 

9270 
9270 

Light  .... 

Hinged  Ends.  .  . 

13500 

12610 

117801111010530 

9950 

9410    8960 

8420 

r  =  4-2« 

Round  Ends  

12830 

11840 

109001  10140 

9410 

8710 

8040,  7530 

6950 

1   0" 

Fixed  Ends... 

13840 

13030 

1214011490 

10950 

10430 

99L'0 

9430 

8960 

Flat  Ends  
Heavy  1  Hinged  Ends.  .  . 

1384013080 

1335012460 

12  140  11  490  10950!  10430 
1151010820102301  9680 

9920    9430 
9140    8600 

8960 

r-s-94  [Round  Ends.... 

1267011670 

10600 

9780 

9050    8370    7720;  7140 

6580 

TABLE   OF   STRUTS. 


125 


No.  3. 
PENCOYD  I  BEAMS  AS  STRUTS. 

|A 


-C-- 


--D. 


In  the  marginal  columns  r  indicates  the  radius  of  gyration  taken  around 
axis  A  B.  When  strut  is  hinged  the  pins  are  supposed  to  lie  in  the  direc- 
tion A  B.  Under  the  conditions  stated  the  strut  may  be  considered  flat 
ended  in  direction  A  B. 


LENGTH  IN  FEET. 

CONDITION 

OF 

SIZE 

OF 

26 

28 

30 

32 

34 

36 

38 

40 

42 

ENDS. 

BEAM. 

10600 

10260 

9920 

9510 

9190 

8880 

8580 

8330 

8140 

Fixed  Ends... 

1  K" 

10600 

1  02(50 

9920 

9510  9190 

8880  8580  8320  8120  Flat  Ends 

10 

9860 
8600 

9.500 
815U 

9140 

772U 

8690 
7240 

8330 
6S50 

8000 
6490 

7670 
6130 

7370 
5810 

7100 
5420 

Hinged  Ends... 
Round  Ends  

Heavy. 

r==  6-86 

10690 

10340 

10000 

9680 

9350 

9040 

8730 

S420 

8230 

Fixed  Ends... 

1  £" 

10690 

10340 

10000 

8680  9350 

9040 

8730 

8420  8220  Flat  Ends  

10 

9950 

9590 

9230 

8870!  8510 

8160 

7830 

7500;  7240  Hinged  Ends.  .  . 

Light. 

8710 

8260 

7820 

743C  7040 

6670 

6310 

5950 

5660 

Round  Ends  

r  -=  8-88 

9430 

9040 

8650 

8330,  8090 

7860 

7630 

7410 

7190 

Fixed  Ends... 

19" 

9430 

9040 

8650 

83201  8070 

7830  i  7590 

7330 

7020  Flat  Ends  

L4 

8600 
7140 

8160 
6670 

7750 
6220 

73"  0 
5810 

704U 
5350 

6720 
5100 

6410 
4760 

6100 
4440 

5800 
4150 

Hinged  Ends... 
Round  Ends  

Heavy. 

r  =  4-69 

9590 

9190 

8800 

8420 

8180 

7950 

7720 

7500 

7280 

Fixed  Ends  

19" 

9590 

9190 

8800 

8420  8170 

7920  7680 

7450;  7140 

Flat  Ends... 

1  ~j 

8780 

8830 

7910 

7500  7170 

6840;  6530 

6220!  5920  Hinged  Ends.  .  . 

Light. 

7330 

6850 

6400 

5950 

5490 

5230 

4890 

4560 

4270 

Round  Ends  

I  =4-78 

8800 

8420 

8140 

7860 

7590 

7320 

7070 

6S70 

6620 

Fixed  Ends... 

1  ft  1  " 

8800 

8420 

8120 

7830 

7540  7210  6840 

6550 

6210 

Flat  Ends  

•i-'Vj 

7910 

7500 

7100 

6720 

6340  5980  5620 

5340 

5010 

Hinged  Ends... 

Heavy. 

6400 

5950 

5420 

5100 

4690 

4320 

3980 

3710 

3390 

Round  Ends  

r  =  4-34 

8800 

8420 

8090 

7810 

7540 

7320 

7070 

6870 

6620 

Fixed  Ends  

,, 

8800 

8420 

8070 

7780 

7500  7210!  6840 

6550 

6210 

Flat  Ends  

J  Uf 

7910 

7500 

7040 

6650 

6280  £980  5620  5340 

5010 

Hinged  Ends... 

Light. 

6400 

5950 

5350 

5030 

4630 

4320 

3980 

3710 

3390 

Round  Ends...  . 

r  =  4-26 

8500 

8180 

7900 

7630 

7320 

7070 

6830 

6580 

6310 

Fixed  Fnds  

1  fj" 

8500  8170 

7870 

7590 

7210  6840  6490J  6160 

5880 

Flat  Ends  

1  U 

7580  7170 

6780 

64101  5980  5620  5280  4960 

4670 

Hingc-d  Ends... 

Heavy. 

6040  5490  5160 

4760J  4320  3980  3650  3340 

3050 

Round  Ends.  .  .  . 

r  —  3-94 

126  WROUGHT  IRON  AND  STEEL. 

No.  4. 
PENCOYD  I  BEAMS  AS  STRUTS. 

GREATEST   SAFE   LOAD  IN   LBS.    PER   SQUARE  INCH   OF   SECTION. 

When  the  struts  are  secure  from  failure  in  the  direction  of  the  flanges  and 
can  bend  only  in  the  direction  of  the  web  C  D.  Using  factors  of  safety 
given  in  previous  tables. 


SIZE 

CONDITION 

LENGTH  IN  FEET. 

OF 

BEAM. 

OP 

ENDS. 

6 

8 

10 

12 

14 

16 

18 

20 

22 

1  0" 

Fixed  Ends  

13840 

13030 

12270 

11670 

11130 

10600 

10090 

9590 

1U 

Light  .  .  . 

Flat  Ends 

13840 
13350 

13030  12270;  116701  11  130  10600 
12460I11650H101010420    9860 

10090 
9320 

9590 

8780 

Hinged  Ends 

r  —  4-05 

Round  Ends. 

12670 

11670 

10750 

10020    9290 

8600 

7930 

7330 

Q" 

Fixed  Ends  

14380 

13430 

12650 

11760 

11130  10600 

10000 

9510 

8960 

V 

Flat  Ends.     ... 

14380 

13430 

12650  11  760!  11  130 

10600  10000 

9510 

8960 

Heavy.  .  .  . 

Hinged  Ends.  .. 

13940 

12900 

12(  50  11110  10420 

9860    9230 

86fO 

8080 

r  =  3-62 

Round  Ends  — 

13330 

12170 

1121010140 

9290 

8600 

7820 

7240 

6580 

Q" 

Fixed  Ends.... 

14380 

13570 

1265011890 

11220 

10690  10090 

9590 

9040 

C7 

Flat  Ends  

14:380 

13570 

1-2650,1189011220 

10690  1(1090  !  9590 

9040 

Light  .... 

r  =  3-66 

Hinged  Ends... 
Round  Ends  

13940 
13330 

13050 
12330 

12050 
11210 

11240 
10290 

10520 
9410 

9950 
8710 

9320 
7930 

8780 
7330 

8160 
6670 

Q" 

Fixed  Ends... 

14110 

13030 

12140 

11310 

10690 

lOfOO 

9430 

8800 

8330 

o 

Flat  Ends  

14110  130301  121401  11310  10690  10000   9430:  8800 

8320 

Heavy  — 

Hinged  Ends... 

13640 

12460  11510 

10620    9950 

9230    86001  7910 

7370 

r  =3-21 

Round  Ends  

13000 

11670 

10600 

9530 

8710 

7820 

7140 

6400 

5810 

Q" 

Fixed  Ends  

14110  13160 

12140 

11400 

10690 

10090 

9510 

8880 

8370 

o 

Flat  Ends  

14110 

13160 

12140 

11400  10690 

10(90    1510    88K) 

8370 

Light  .... 

Hinged  Ends... 

13640 

1261011510 

10720    9950 

9350 

8690   8000 

7430 

r^  3.  us 

Round  Ends  

13000 

11840 

10600 

9660 

8710 

7930 

7240 

6490 

5880 

7" 

Fixed  Ends  

13570 

12400 

11400 

10690 

9920 

9190 

8500 

8090 

7380 

I 

Flat  Ends  113570 

12400 

11400i  10690 

9920 

9190 

8500,  8070 

7640 

Heavy  — 

Hinged  Ends.  .. 
Round  Ends  

13050 
12330 

11780 
10900 

10720 
9660 

9950 
8710 

9140 
7720 

8380 

6850 

7580 
6040 

7040 
5350 

6470 
4830 

7" 

Fixed  Ends  

13700 

12650 

11580 

10860 

10170 

9510 

8800 

8280 

7900 

I 

Flat  Ends  

137001265011580 

1086010170 

95101  8800    8270 

7870 

Wtw 

Hinged  Ends.  .. 
Round  Ends  — 

1S2WO  12050  10910 
1250011210    9900 

10130)  9410    8690]  7910    7300 
8930    8040    7240    6400J  5730 

6780 
5160 

TABLE   OF  STRUTS. 


127 


No.  4. 

PENCOYD  I  BEAMS  AS  STRUTS. 
U 


-c- 


|B 

In  the  marginal  columns  r  indicates  the  radius  of  gyration  taken  around 
axis  A  B.  When  strut  is  hinged  the  pins  are  supposed  to  lie  in  the  direc- 
tion A  B.  Under  the  conditions  stated  the  strut  may  be  considered  flat 
ended  iu  direction  A  B. 


LENGTH  IN  FEET. 

CONDITION 

SIZE 

24 

26 

28 

30 

32 

34 

36 

38 

40 

OF 

ENDS. 

OF 

BEAM. 

9110 

81550 

8280 

8000 

7720 

7450 

7190 

6990 

6750 

Fixed  Ends... 

10" 

9110 

8650 

8270  7970 

7680 

7390 

7020 

6720 

6370  Flat  Ends  

1  \J 

8250 

7750 

7300 

6910 

6530 

6160 

5800 

5500 

5170  Hinged  Ends... 

Light. 

6760 

6220 

5730 

5200 

4890 

4500 

4150 

3870 

3540 

Round  Ends  .  .  . 

r  =4-05 

8420 

8140 

7810 

7540 

7240 

69,50 

6710 

6400 

6090 

Fixed  Ends... 

0" 

84-20 

8120 

7780 

7500  7080 

6660 

6310 

5970 

5650  Flat  Ends  

V 

7500 

7100 

6650 

6280!  5860 

5450 

5110 

4770 

4440  Hinged  Ends.. 

Heavy. 

5950 

5420 

5030 

4630 

4210 

3810 

3490 

3150 

2820 

Round  Ends  

i  =  s-ea 

8580 

8180 

7900 

7590 

7320 

7030 

6790 

6490 

6170 

Fixed  Ends... 

Q" 

8580 

8170 

7870!  7540 

7210  6780 

6430 

6070 

5740  Flat  Ends... 

t7 

7670 

7170 

6780!  6340 

5980!  5560 

5220 

4860 

4530  Hinged  Ends... 

Light. 

6130 

5490 

5160 

4690 

4320  3920 

3600 

3240 

2910  Round  Ends.... 

r  —  3-63 

7950 

7630 

7280 

6990 

6670  6350 

6010 

5710 

5430 

Fixed  Ends... 

0" 

7920 

75:iO 

7140 

6?20  6260  5930 

5560 

5230 

4880  Flat  Ends... 

o 

6840 

6410 

5920 

5500 

5030 

47'20 

4350 

4010 

3620  Hinged  Ends... 

Heavy. 

5230 

4760 

4270 

3870 

3440 

3100 

2730 

2430 

2150 

Round  Ends  

r  ="  3-21 

8000 

7680 

7320 

7030 

6750 

6400 

6090 

5500 

5510 

Fixed  Ends... 

Q" 

7970 

7640  7210'  6730 

6370 

5970 

5650 

5340  4<)80Flat  Ends  

O 

6910 

64701  5980  5560 

5170 

4770 

4440  4120 

3730  Hinged  Ends... 

Light. 

5200 

4830 

4320 

3921) 

3540 

3150 

2820 

2510 

2230  1  Round  Ends.... 

r  =3-25 

7280 

6950 

6580 

6110 

5800 

5470 

5110 

4740 

4370:  Fixed  Ends... 

hn 

7110 

6660 

6160  5740'  5340:  4930 

4490 

4090 

3710  Flat  Ends  

( 

5920 

54,50 

4960  4530  4120!  3680 

3210 

2800 

2440  Hi  used  Ends... 

Heavy. 

4270 

3810 

3340 

2910 

2510 

2190 

1860 

1620 

1420 

Round  Ends  — 

I  =  2-75 

7500 

7150 

6830 

6440 

6090 

5750 

5430 

5070 

4740 

Fixed  Ends  .  .  . 

H" 

7450 

(5960 

6490  6020  5650 

5280 

48SO 

4440 

4090:  Flat,  Ends  

I 

6220 
4560 

5740 
4090 

5280  4820  !  4440 
3650  3200  2820 

4060 
2470 

362o 
2150 

3160 
1830 

280i  (Hinged  Ends... 
1620  Round  Ends.  .  . 

rLjght.9 

128  TABLES  OF  STRUTS. 

No.  5. 

PENCOYD  I  BEAMS  AS  STRUTS. 

GREATEST  SAFE  LOAD  IN  LBS.    PEE  SQUARE  INCH  OF  SECTION. 


When  the  struts  are  secure  from  failure  in  the  direction  of  the  flanges,  and. 
can  bend  only  in  the  direction  of  the  web  C.  D.  Using  factors  of  safety 
given  in  previous  tables. 


SIZE 

CONDITION 

LENGTH  IN  FEET. 

OP 

BKAM 

OP 
TT-wTia 

JjjNDS. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

6" 

Fixed  Ends 

14240 

12900 

11  580 

10690 

9840 

8960 

S9sn 

7810 

Flat  Ends 

14240 

12900  '11580 

10690    9840 

8960   8270 

7780 

Heavy  — 

r  =  2-31 

Hinged  Ends... 
Round  Ends  



13790 
13160 

1232010910 
11520J  9900 

9950 
8710 

9050 
7630 

8080 
6580 

7300 
5730 

6650 
5030 

6" 

Fixed  Ends 

14380 

13030 

mfio 

10050 

10090 

9270 

8KOO 

8000 

Flat  Ends  

1  WS;t 

13030  11760  \  10950  10090 

9270    8500 

7970 

Light.  .  . 

Hinged  Ends 

113340 

12460  11110  102301   93-20 

8420    7580 

6910 

I   =-  2-4S 

Round  Ends.  .  .  . 

13330 

11670 

10140 

9050 

7930 

6950    6040 

5200 

5" 

Fixed  Ends 

13840 

13840 

12270 
12270 

1104010000 
1104010000 

9040 
9040 

8230    7680 
8220;  7640 

7110 

6900 

Flat  Ends... 

__ 

Heavy  'Hin<rpri  TCnrls 

133:>i> 

11650 

10330    9230    8160 

7240    6470 

5680 

r  =  1  •»» 

Round  Ends 

12670 

10750 

9170 

7820    6670 

5660    4830 

4030 

K" 

Fixed  Ends.... 

14110 

12650 

11400 

10340    9430 

85801  8000 

7500 

«J 

Flat  Ends  

14110 

12650 

1140010340    9430 

8580    7970 

7450 

Liffht 

Hinged  Ends 

13640 

12050  10720'  95901   «Km 

7670    MI  in 

6220 

r  =  2-0«° 

Round  Ends  .  .  . 

1300011210 

9660 

8260 

7140 

6130 

5200 

4560 

| 

4" 

Fixed  Ends 

1316011400 
13160  11400 

10090 
10090 

8880 
8880 

8040 

8020 

7370 

7270 

6750 
6370 

6130 
5700 

Flat  Ends     

Heavy  

Hinged  Ends.. 

12610  10720 

9320    8000 

6970 

6040 

5170 

4480 

r  =  1-63 

Round  Ends.  . 

11840    9660 

7930 

6490 

5270 

4380 

3540 

2870 

A" 

Fixed  Ends... 

13160  11400 

10170 

8960 

8090 

7410 

6830 

6170 

T: 

Flat  Ends  

1316011400 

10170    8960 

8070    7330 

6490 

5740 

Light.  .  . 

Hinged  Ends  

12610  10720 

9410i  8080 

7040!  6100 

5280 

4530 

r  =   1-63 

Round  Ends  

11840 

9660 

8040 

6580 

5350 

4440 

3650 

2910 

0" 

Fixed  Ends... 

1438ol  11760 

10000 

8500 

7540 

6710 

5840 

5030 

4210 

o 

Flat  Ends  j  143801  1  1760  10000 

8500    7500 

6310 

5380 

4390 

3540 

Heavy.  .  .  . 

Hinged  Ends.  .  .  \  13940  11110    9230 

7580    6280 

5110 

4160J  3110 

2280 

r  =1-21 

Round  Ends  

13330 

10140 

7820 

6040 

4630 

3490 

2550 

1790 

1330 

0" 

Fixed  Ends  

14520 

12010 

10170 

8650 

7680 

6870    6050 

5230 

4450 

o 

Light  

Flat  Ends  
Hinged  Ends... 

14520  12010  10170 
14090  11380    9410 

8650    7640 
7750    6470 

6550    5610    4630 
5340    4390|  3360 

3790 
2520 

*  =  1-26 

Round  Ends  

13500 

10440,  8040 

6220    4830 

3710 

2780 

1970 

1460 

TABLES   OP  STKUTS. 


No.  5. 
PENCOYD  I  BEAMS  AS  STRUTS. 

|A 
I 


129 


LB 

In  the  marginal  columns  r  indicates  the  radius  of  gyration  taken  around 
axis  A.  B.  When  strut  is  hinged  the  pins  are  supposed  to  lie  in  the  direc- 
tion A.  B.  Under  the  conditions  stated  the  strut  may  be  considered  flat 
ended  in  direction  A.  B. 


LENGTH  IN  FEET. 

CONDITION 

SIZE 

20 

22 

24 

26 

28   30 

32 

34 

36 

OF 

ENDS. 

OP 

BEAM. 

7320 

6910 

6440 

C010 

5590  5150 

4740  4290 

3930 

Fixed  Ends... 

7210 

6600 

(5020 

5560 

5080  4540 

4090  3620 

3280  Flat  Ends  

O 

5980 

5390 

4820 

4350 

3840  3260 

2800  23(50 

2080  Hinged  Ends... 

Heavy. 

4320 

3760 

3200 

2730 

2310 

1900 

1620  1370 

1190 

Round  Ends  .  .  . 

r  =  2-31 

7540 

7110 

6710 

6310 

5880 

5470 

5070  4650 

4250  Fixed  Ends... 

a" 

7500 

6900 

6310 

5880 

5430 

4930  4440  4000 

3580  Flat  Ends  

O 

6280 

5680 

5110 

4670 

4210 

3680  3160  2720 

2320  Hintred  Ends... 

Light. 

4630 

4030 

3490 

3050 

2600 

2190  1830  1570 

1350 

Round  Ends  

r  «  2-43 

6620 

6090 

5590 

5110 

4610 

4130  3730  3340 

2970 

Fixed  Ends... 

5" 

6210 

5650 

5080 

4490 

3960 

3460  3100  2780 

2500  Flat  Ends  

' 

5010 
3390 

4440 

2820 

3840 
2310 

3210 
1860 

2680  2220 
1550  1290 

1950 
1100 

1690 
940 

1450 
820 

Hinged  Ends... 
Round  Ends  

Heavy. 

r  =-  1-99 

7030 

6580 

6090 

5630 

51501  4090 

4250  3860 

3500 

Fixed  Ends.... 

5" 

6780 

6160 

5650 

5130 

4540 

4040 

3580  3220 

2900 

Flat  Ends  

5560 
3920 

4960 
3340 

4440 

2820 

3900 
2350 

3260 
1900 

2760 
1590 

2320  2040 
1350  1160 

1800 
1000 

Hinged  Ends... 
Round  Ends  

Light. 

r  =2-08 

5510  4910 

4290 

3790 

3310 

2850 

2500  2180 

1900 

Fixed  Ends  

A" 

4980  |  4260 

3620  3160 

2760 

2420 

2140  1910 

1680 

Flat  Ends  

•± 

3730!  2970 

2360  1990 

1670 

1380 

1180 

1040 

900 

Hinged  Ends... 

Heavy. 

2230 

1710 

1370 

1130 

930 

780 

670 

600 

520 

Round  Eiids.  .  .  . 

r  =  1-63 

5590 

5000 

4410 

3860 

3400 

2940 

2570 

2240 

1930 

Fixed  Ends  

4t  f 

5080  4350 

3750  3220 

2830 

2480 

2190 

1950 

1720 

Flat  Ends  

3840  3060 

2480  2040 

1730 

1430 

1220 

1070 

920 

Hinged  Ends... 

Light. 

2310  1760 

1440 

1160 

960 

810 

690 

610 

540 

Round  Ends  

r  =1.65 

3560  2940 

2450 

2000 

1740 

1520 

1320 

1120 

990 

Fixed  Ends... 

0" 

2950  2480 

2100  1780 

1490  1220 

1000 

820 

670  Flat  Ends  

o 

1840 
1030 

1430 

810 

1160 
660 

960 
560 

800  680 
450  370 

590 
320 

500 
260 

420  Hinged  Ends... 
230  Round  Ends  

Heavy. 

r  =  1-21 

3760 

3150 

2R10 

2180 

1850 

1630 

1420 

1220 

1060 

Fixed  Ends... 

0" 

3130 

2640 

2230;  1910 

1620 

1350  1110  900 

750  Flat  Ends  

O 

1970 

1570 

1240  1040 

870 

740 

630  ;  550 

460  Hinged  Ends... 

Lieht. 

1120 

880 

710  600 

500 

410 

350  290 

240|Round  Ends  

r  =  1-26 

130  TABLES  OF  STEUTS. 

No    6. 
PENCOYD  I  BEAMS  AS  STRUTS. 

GREATEST  SAFE  LOAD  IN  LBS.   PER  SQUARE  INCH  OF  SECTION. 


When  the  struts  are  free  to  bend  at  right  angles  to  the  web  ;  or  in  the 
weakest  direction  C.  D.    Using  factors  of  safety  given  in  previous  tables. 


SIZE 

OP 

BEAM. 

CONDITION 

OP 

ENDS. 

LENGTH  IN  FEET. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

15" 

Fixed  Ends.... 

14380 

11760 

10000 

8420 

7500 

6670 

5800 

5000 

4170 

-L  V 

Flat  Ends 

14380  11760 

10000 

8420 

7450 

6260 

5340 

4350 

3500 

Heavy  — 

r=  1-20 

Hinged  Ends... 
Round  Ends  

13940111110 
1333010140 

9230 

7820 

7500 
5950 

6220 
4560 

5G60 
3440 

4120 
2510 

306! 
1760 

2250 
1310 

1  V 

Fixed  Ends  

1411011400 

9439 

8000 

7030 

6090 

5150 

4250 

3500 

J.  *J 

Light  

Flat  Ends  
Hinged  Ends... 

1411011409 
13640  10720 

9433 
8630 

7970 
6910 

6780 
5560 

5650 
4440 

4540 
3260 

358( 

2323 

2900 
1800 

r=  1-08 

Round  Ends  

13000 

9660 

7140 

5200 

3920 

2820 

1900 

1350 

1000 

10" 

Fixed  Ends... 

14240 

11670 

9840 

8330 

7370 

6530 

5630 

4820 

4000 

&.£! 

Flat  Ends  

14240 

11670 

9840 

8320 

7270 

6110 

5130 

4170 

3340 

Heavy  — 

Hinged  Ends..  . 

13790 

11010 

9059 

7370 

6040 

4910 

3900 

2890 

2130 

r  =  1-17 

Round  Ends  

13160 

10020 

7630 

5810 

4380 

3290 

2350 

1660 

1230 

10" 

Fixed  Ends... 

13840 

11040 

9110 

7720 

6710 

5670 

4740 

3830 

3060 

I  — 

Flat  Ends  

13840 

11049 

9110 

7680 

6310 

5180 

4090 

3190 

2570 

Light  .... 

Hinged  Ends.  .. 

13350 

10339 

8250 

6530 

5110 

39501  2800 

2020 

1510 

r  =  1-01 

Round  Ends  

12670 

9170 

6760 

4890 

3490 

2390 

1620 

1150 

850 

10-i" 

Fixed  Ends  
Plat  Ends  

14380 
143  0 

11760 

1176C 

10000 
100CO 

8370 

8370 

7450 
7390 

6620 
6210 

57HO 

5280 

4950 
4300 

4130 
3460 

Heavy,  .  .  . 

Hinged  Ends... 

13910 

11110 

9230 

7439 

6160 

5010 

4060;  3010 

2220 

r  =  1-19 

Round  Ends  

13330 

10140 

7820 

5880 

4500 

3390 

2470 

1730 

1290 

101  " 

Fixed  Ends  

13840 

10950 

8960 

7590 

6580 

5510 

4530 

3630 

2880 

Flat  Ends  

13840  10950 

8960 

7540 

6160 

4989 

3870 

3010 

2440 

Light  

Hinged  Ends... 

1335010230    8080    6340 

4960 

37:30 

8600 

1880 

1400 

r  =  «87 

Round  Ends  

12670    9050 

| 

6580 

4690 

3340 

2230 

1500 

1060 

790 

10" 

Fixed  Ends  ... 

13S4o'  10950 

8960 

7590 

6580 

5510 

4530 

3630 

2880 

L\J 

Flat  Ends  

1384010950    8960 

7540 

6160   4980 

3870 

3010 

2440 

Heavy.  .  . 

Ringed  Ends  .  .  . 

1*350  10230 

80SO 

6340 

49601  3730 

2600 

1880 

1400 

I  =    -98 

Round  Ends  

12670    9050 

6580 

4690 

33401  2230 

1500 

1060 

790 

I 

TABLES  Or  STRUTS. 


3  31 


No.  6. 
PENCOYD  I  BEAMS  AS  STRUTS. 

L 


!" 

In  the  marginal  columns  r  indicates  the  radius  of  gyration  taken  around 
axis  A.  B.  When  the  strut  is  hinged  the  pins  are  supposed  to  lie  in  the  di- 
rection A.  B.  If  the  pins  lie  in  the  direction  C.  D.  consider  the  strut  flat 
ended  by  this  table. 


LENGTH  IN  FEET. 

CONDITION 

SIZE 

20 

22 

24 

26 

28 

30 

32 

34 

36 

OF 

ENDS. 

OP 

BEAM. 

3500 

2880 

2410 

1960 

1720 

1500 

1290 

1090 

980 

Fixed  Ends... 

15" 

2900 

2440 

2070 

1750 

1460 

1200 

970 

800 

650  Flat  Ends  

10 

1800 
1000 

1400 
790 

1140 
650 

940 
550 

790 

440 

670 
370 

580 
320 

490 
260 

420 
230 

Hinged  Ends... 
Round  Ends  

Heavy. 

r  =  1-20 

2830 
2400 

2310 

2000 

1870 
1650 

1620 
1340 

1380 
1060 

1160 
820 

1000 
670 

860 
520 

740 
430 

Fixed  Ends  
Flat  Ends 

15" 

1370 

1100 

890 

730 

610 

520 

430 

340 

280 

Hinged  Ends... 

Light. 

770 

630 

510 

410 

340 

280 

230 

200 

170 

Round  Ends.  .  .  . 

r  =  1-08 

&340 

2780 

2730 
2320 

2270 
1970 

1870 
1650 

1640 
1360 

1410 
1100 

1210 

890 

1040 

720 

920 

580 

Fixed  Ends  
Flat  Ends... 

12" 

1690 

1310 

1080 

890 

740 

630 

540 

450 

380  Hinged  Ends... 

Heavy. 

940 

740 

620 

510 

410 

350 

290 

240 

210 

Round  Ends  — 

r  =  I'll 

£450 

1940 

1660 

1400 

1160 

1000 

850 

720 

Fixed  Ends.... 

10" 

2100 

1730 

1390 

1090 

850 

670 

510 

410 

Flat  Ends  

JL  -i 

1160 

930 

760 

620 

520 

430 

340 

270 



Hinged  Ends... 

Light. 

660 

540 

420 

350 

280 

230 

200 

160 

Round  Ends  

r  =  1-01 

3430 

2830 

2360 

1930 

1690 

1470 

1260 

1070 

960 

Fixed  Ends  

101" 

2850 
1750 
970 

2400 
1370 
770 

2d30 
1120 
640 

1720 
920 
540 

1430 
770 
430 

1170 
660 
360 

940 
560 
310 

770 
470 
250 

620 
400 
220 

Flat  Ends  
Hinged  Ends... 
Round  Ends  

Heavy. 

r=»  I-M 

2290 

1850 

1560 

1310 

1070 

930 

780 

670 

Fixed  Ends  

i  n  i  " 

1990 

1620 

1270 

990 

770 

600 

460 

380 

Flat  Ends  .  .  . 

lU^r 

1090 

870 

700 

580 

470 

390 

300 

240 

HingedEnds... 

rL-^?7 

620 

500 

390 

320 

250 

210 

170 

150 

Round  Ends.  .  .  . 

2290 

1850 

1560 

1310 

1070 

930 

780 

670 

Fixed  Ends... 

1  f\tt 

1990 

1620 

1270 

990 

770 

600 

460 

380 

'.'.  Flat  Ends  

JL  W 

1090 
620 

870 
500 

700 
390 

580 
320 

470 
250 

390 
210 

300 
170 

240 
150 



Hinged  Ends... 
Round  Ends.... 

Heavy. 

r  =  -98 

132  TABLES  OF  STKUTS. 

No.  7. 
PENCOYD  I  BEAMS  AS  STRUTS. 

GREATEST  SAFE  LOAD  IN  LBS.    PER  SQUARE  INCH  OF  SECTION. 

The  strut  is  supposed  to  be  free  to  bend  in  the  weakest  direction  C.  D. 
The  radius  of  gyration  is  taken  around  A.  B. 


SIZE 

OK 

CONDITION 

LENGTH  IN  FEET. 

BEAM. 

OF 

ENDS. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

10" 

Fixed  Ends... 
Flat  Ends  

1370010770 
13700  10770 

8730 
8730 

7450 
7390 

6400 
5970 

5310 

4730 

4290 
3620 

3430 

2850 

2710 
2300 

Liirht  .  . 

r  "=  -95 

Hinged  Ends... 
Round  Ends  

13200 
12500 

10040 
•,  8820 

7839 
6310 

61(50 
4500 

4770 
3150 

3460 
2040 

1  2360 
1370 

1750 
970 

1300 
740 

9" 

Fixed  Ends  

13700 

10860 

8800 

7500 

6440 

5390 

4370 

3500 

2760 

t/ 

Flat  Ends  

137001  10860 

8800 

7450 

6020 

4830 

3710 

2900 

2340 

Heavy  — 

Elinged  Ends.  .. 

13200 

10130 

7910 

6220 

4820 

3570 

2440 

1800 

1330 

r  =  -98 

Round  Ends  

12500 

8930 

6400 

4560 

3200 

2120 

1420 

1000 

750 

9" 

Fixed  Ends.... 

13430 

10520 

8370 

7150 

6010 

4910 

3860 

3000 

2340 

u 

Flat  Ends  

13430 

10520 

8370 

6960 

5560 

4260 

3220 

2530 

2020 

Light  

iinged  Ends... 

12900 

9770 

7430 

5740 

4350 

2970 

2040 

1470  1110 

r  =  -89 

Round  Ends  

12170 

8490 

5880 

4090 

2730 

1710 

1160 

830  630 

C" 

r^ixed  Ends  

13."70 

10770 

8650 

7410 

6310 

5270 

4210 

3370  i  2640 

o 

?lat  Ends  

l.:57)  10770 

8659 

7339 

5880 

4680 

3540  2800!  2250 

Heavy  

ttngedEnds... 

1305J 

10040 

7750 

6100 

4670 

3410 

2280 

17101  1260 

r  =  •»! 

Sound  Ends  

12330 

8820 

6220 

4440 

3050 

2010 

1330 

950 

720 

C" 

Fixed  Ends... 

3430 

10430 

8330 

7110 

5960 

4820 

3790 

2940 

2290 

o 

Hut  Ends  

3439 

10430 

8320 

6900 

5520 

4170 

3160 

2480!  1990 

Light  

linged  Ends... 

9900 

9680 

7370 

5680 

4300 

2899 

1990 

1430  1090 

r  —  '68 

Round  Ends  — 

2170 

8370 

5810 

4030 

2690 

1660 

1130 

810 

620 

Hit 

<Mxed  Ends  

3930 

99  ?0 

7990 

6620 

5310 

4100 

3990 

2340 

1800 

t 

Hat  Ends  

:5  i:jo 

9920 

7870 

6210 

4730 

3430 

2600 

2020  1560 

Heavy  

lingedEnds... 

2460 

9140 

6780 

5010 

3469 

2200 

1530 

1110  840 

r  =  -79 

lound  Ends  

1670 

7720 

5160 

3390 

2040 

1270 

860 

630J  480 

Hit 

Fixed  Ends.... 

3160 

10090 

8040 

6790 

5550 

4330 

3340 

2540  1920 

I 

Flat  Ends  

3160 

10090 

8020 

6430 

5039 

36«0 

2780 

2170'  1700 

Light.  .  .  . 

fringed  Ends... 

2610 

9320 

6H70 

5220 

3790 

2400 

1690 

1210  910 

r  =  -82 

Round  Ends  

1840 

7930 

5270 

3600 

2270 

1390 

940 

690 

530 

TABLES  OF  STBUTS. 


133 


No.  7. 
PENCOYD  I  BEAMS  AS  STRUTS. 


A.  B.  indicates  the  direction  of  pins  for  hinged  struts  in  this  table.  If  the 
pins  are  placed  in  the  direction  6'.  D.  consider  the  strut  as  flat  ended,  r  in 
marginal  columns  inclica  es  radius  of  gyration  around  A.  B. 


LENGTH  IN  FEET. 

CONDITION 

OF 

ENDS. 

SIZE 

OP 

BEAM. 

20 

2110 

I860 
1010 
580 

2180 
1910 
1040 

600 

1840 
1610 

870 
500 

2070 
1830 
990 
570 

1800 
1560 
840 
480 

1450 
1150 
650 
3GO 

1570 
1290 
710 
390 

22 

24 

1460 
1160 
650 
360 

1500 
1200 
670 
370 

1250 
930 
560 
300 

1430 
1120 
K40 
350 

1220 
900 
550 
290 

950 
610 
400 

220 

1030 
710 
440 
230 

26 

28 

30 

850 
510 
340 
200 

880 
540 
360 
200 

720 
410 
270 
160 

830 
490 
330 
190 

700 
400 
250 
160 

32 

34 

36 

1740 
1490 
800 
450 

1780 
1530 
S30 
470 

1530 
1230 
680 
380 

1700 
1440 
780 
430 

1500 
1200 
67'0 
370 

1150 
840 
£20 
270 

1270 
950 
570 
310 

1210 
890 
540 
290 

1240 
920 
560 
300 

1030 
710 
440 
230 

1170 
860 
530 
280 

1010 
680 
430 
230 

770 
450 
290 
170 

850 
510 
340 
200 

1020 
690 
440 
230 

1040 
720 
450 
240 

860 
520 
340 
200 

990 
670 

420 
230 

840 
500 
330 
190 

720 
410 
270 
160 

740 
430 
280 
170 





Fixed  Ends  
Flat  Ends  
Hinged  inds... 
Round  Ends  

Fixed  Ends... 
Flat  Ends     . 

10" 

,LI**i 

9" 

Heavy. 

r  =='  -9« 

9" 

Light. 

r  =   -89 

8" 

Heavy. 

8" 
,L»'.-, 

1" 

Heavy. 

r  =   -79 

r 
,w.i 



Hinged  Ends... 
Round  Ends  

Fixed  Ends  
Flat  Ends  
Hinjred  Ends... 
Round  Ends  

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  Ends  

Fixed  Ends.... 
Flat  Ends  
Hinged  Ends... 
Round  Ends  — 

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  Ends  

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  Ends  

700 
400 
250 
160 

700 
400 
250 
1HO 

134  TABLES   OF  STRUTS. 

No.  8. 
PENCOYD  I  BEAMS  AS  STRUTS. 

GREATEST   SAFE  LOAD  IN  LBS.  PER   SQUARE  INCH  OF  SECTION. 

(See  remarks  at  head  of  Tables  No.  6  and  7.) 


SIZE 

CONDITION 

LENGTH  IN  FEET. 

OK 

BEAM 

OP 

ENDS. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

fi" 

Fixed  Ends  

12140 

8880 

7030    5470 

4000 

2830 

2000 

1550 

1170 

O 

Flat  Ends  

12140 

8880 

6780    4930 

3340 

2400 

1180 

1260 

860 

Heavy  

Hinged  Ends... 

11510 

8000 

5560    3680 

2130 

1370 

960 

700 

530 

r  =   -65 

Round  Ends  

10600 

6490 

3920 

2190 

12,0 

770 

560 

390 

2SO 

a" 

Fixed  Ends  

12270 

8960 

7110 

5590 

4100 

2940 

2090 

1590 

1220 

o 

Flat  Ends 

12270 

8960 

6900    5080 

3430 

2480 

1840 

1310 

900 

Light  .... 

Hinged  Ends... 

11650 

8080 

5680    3840 

2200 

1430 

1000 

720 

550 

r  =-  -68 

Round  Ends  — 

10750 

6580 

4030 

2310 

1270 

810 

580 

400 

290 

K" 

Fixed  Ends.... 

11760 

8420 

66701  5000 

3500 

2410 

1720 

1290 

980 

u 

Flat  Ends  

11760 

8420 

6260 

43501  2900 

2070 

1460 

970 

650 

Heavy  — 

Hinged  Ends... 

11110 

7500 

50CO 

30601  1800 

1140 

790 

580 

420 

r  =  -60 

Round  Ends  

10140 

5950 

3440 

1760 

1000 

650 

440 

320 

230 

K" 

Fixed  Ends.... 

11760 

8420 

6670 

5000 

3500 

2410 

1720 

1290 

980 

t_J 

Flat  Ends    

11760 

8420 

6260 

4350  !  2900 

207'0 

1460 

970 

650 

Light  

Hinged  Ends... 

11110 

7500 

5060 

2C60    1800 

1140 

790 

58C 

420 

r  —   -60 

Round  Ends  — 

10140 

5950 

3440 

1760 

1000 

650 

440 

32C 

230 

41  1 

Fixed  Ends  

12010 

8730 

6910 

5310 

3830 

2660 

1870 

144C 

1070 

Flat  Ends  

12010 

8730 

6600 

47301  3190 

2260 

1650 

770 

Heavy  

Hinged  Ends... 

11380 

7830 

5390 

2460    2C20 

1270 

890 

64( 

470 

r*=   -63 

Round  Ends  

10440 

6310 

3760 

2040 

1150 

720 

510 

36C 

250 

A" 

Fixed  Ends  

11130 

7770 

5750 

3890 

2520 

1690 

1200 

87( 

*± 

Flat  Ends  

11130 

7730 

5280 

32-0 

2160 

1430 

880 

53(, 

Light  

Hinged  Ends... 

10420 

6590 

4C60 

2060 

1200 

770 

540 

35C 

r—  -si 

Round  Ends  

9290 

4960 

2470 

1180 

680 

430 

290 

200 



0" 

Fixed  Ends  

11670 

8370 

6620 

4910 

3400 

2310 

1660 

1240 

940 

O 

Flat  Ends  

11670    &370 

6210 

4260 

2830 

2000 

1390 

920 

600 

Heavy.  .  . 

r-=   -59 

Hinged  Ends... 
Round  Ends  

11010 
10020 

7430 

5880 

5010 
3390 

2970 
1710 

1730 
960 

1100 
630 

760 
420 

560 
300 

390 
210 

0" 

Fixed  Ends... 

11310 

7900 

5960 

4130 

2730 

1810 

1320 

960 

710 

O 

Flat  Ends  

11310    7870    5520 

3460 

2320 

1580    1000 

630 

400 

Light  

Hinged  Ends... 

10620 

6780    4300 

2220 

1310 

850     590 

410 

260 

r—  -53 

Round  Ends.  .  .  . 

9530 

5160    2690 

1290 

740 

480     320 

220 

160 

TABLES   OF   STEUTS.  135 


ROLLED  ANGLES  AS  STRUTS. 

Tables  Nos.  9  and  10  apply  to  even-legged  angles  acting  as 
struts.  As  described  in  the  head  notes,  the  angle  is  considered 
free  to  yield  in  its  weakest  direction,  that  is  in  the  direction 
of  the  least  radius  of  gyration. 

If  the  angle  is  prevented  from  failing  in  this  direction,  by 
bracing  or  otherwise,  its  resistance  will  be  increased  to  some  ex- 
tent, and  a  correction  can  be  made  by  taking  the  greatest  instead 
of  the  least  radius  of  gyration  into  the  calculation. 

Example. — An  angle  strut  with  flat  ends,  whose  dimensions 
are  4  x  4  x  |  inches,  and  13  feet  long,  has  a  least  radius  of  gyra- 
tion of  .  81  inch,  and  greatest  radius  of  gyration  1 . 24.  When 

7  144 

the  strut  has  no  lateral  support  the  value  of  —  would  be  —  = 

178.     (See  table  on  page   98.)    By  Table  No.  2  the  safe  load 
would  be  3,580  Ibs.  per  square  inch. 

If  this  strut  it  now  braced  so  that  it  cannot  fail  in  the  weakest 
direction,  that  is  in  the  line  of  a  diagonal  from  the  corner  of  the 
angle,  but  is  free  to  fail  in  the  direction  of  its  legs,  then  the 

I  144 

value  of  —  becomes         •  =  116,  and  the  safe  load  by  the  tables 

becomes  6,500  Ibs.  per  square  inch. 

STRUTS  COMPOSED  OF  SEVERAL  ANGLES. 
If  a  strut  is  composed  of  several  angles,  properly  braced  to- 
gether, so  that  the  angles  cannot  fail  individually,  find  the  least 
radius  of  gyration  of  the  section  in  the  manner  described  on 
page  111,  and  thus  the  working  resistance  of  the  strut  from 
Table  No.  2,  as  described  before. 

3"             Example.—  What  is  the  working  resistance 

^1  of  a  flat-ended  strut  10"  square  outside,  and 

U  18  feet  long,  composed  of  four  3x3  angles 

^ 10" >  connected  by  triangular  bracing  ? 

k  The  radius  of  gyration  as  found  on  page 

, 'I  111,  is  4. 21  inches.     1=51. 

T 

Safe  load  per  square  inch  by  Table  No.  2  =  10,800  Ibs. 


136  WKOUGHT  IRON  AND  STEEL. 

But  the  angles  will  fail  individually  if  the  bracing  is  not  suf- 
ficient. To  determine  the  greatest  distance  apart  for  centres  of 
bracing,  consider  each  angle  as  a  strut  bearing  10,800  Ibs.  per 
square  inch  of  section.  The  least  radius  of  gyration  for  a  single 

angle  is  .  60  inch.     By  Table  No,  2,  the  value  of  —  correspond- 

r 

ing  to  the  pressure  of  10,800  is  51,  as  found  above.  Therefore 
.60  x  51  =  30  inches,  which  is  the  greatest  distance  apart  for 
centres  of  bracing.  For  properly  designed  struts  of  the  fore- 
going section,  the  resistance  per  square  inch  may  be  ascertained 
approximately  by  means  of  table  No.  18,  page  158,  although  the 
former  kind  of  column  should  be  somewhat  stronger  than  the 
latter  per  unit  of  section. 

STRUTS  OF  UNEVEN  ANGLES. 

When  uneven  angles  are  used  as  struts,  find  the  value  of  — 

r 

by  means  of  the  least  radius  of  gyration  as  found  on  page  99, 
and  the  corresponding  resistance  per  square  inch  of  section  by 
table  No.  2  as  before.  If  the  angle  is  braced  in  such  a  manner 
that  failure  cannot  occur  diagonally,  it  will  then  fail  in  the  di- 
rection of  the  shortest  leg,  and  if  braced  in  this  direction  also, 
it  will  be  forced  to  fail  in  the  direction  of  the  longest  leg.  The 
resistance  in  either  direction  can  readily  be  found  by  means  of 
the  respective  radii  of  gyration,  as  given  in  columns  VII,  VIII, 
IX,  page  99. 

It  is  frequently  desirable  to  use  a  pair  of  uneven  angles, 
braced  together  in  the  direction  of  the  shortest  legs. 


Total  length  =  L. 


v\S  \P 

f- -----I' 


For  this  form  the  least  radius  of  gyration  for  the  combined 


TABLES   OF   STEUTS.  137 

sections  will  be  the  same  as  the  greatest  radius  of  gyration  for  a 
single  angle.  Therefore  take  in  the  tables  of  elements  of  un- 
even angles,  the  greatest  radius,  or  that  corresponding  to  axis 
A  B,  when  estimating  the  strength  of  the  combined  sections, 
and  the  least  radius  when  determining  the  distance  between  cen- 
tres of  bracing. 

Example. — A  flat-ended  strut,  16  feet  long,  is  composed  of 
two  uneven  angles,  each  6  x  4  x  ^  inches,  and  4.75  square 
inches  sectional  area.  The  angles  are  braced  together  in  the 
direction  of  the  short  legs.  What  is  the  greatest  safe  load  for 
the  strut,  and  what  the  greatest  distance  between  centres  of 
bracing  measured  on  the  leg  of  the  angle  ? 

By  the  tables  on  page  99,  the  greatest  radius  of  gyration  = 

1.9  inches,  therefore  L  =  101. 

T 

By  Table  No.  2  we  have  for  this  7,450  Ibs.  per  square  inch, 
or  70,700  Ibs.  for  the  whole  strut.  The  least  radius  of  gyration 
is  .92  inch,  which  multiplied  by  101  gives  92.9  inches  as  the 
greatest  distance  between  centres  of  bracing. 

To  find  the  greatest  distance  apart  centres  of  bracing  (I)  should 

be  it  is  only  necessary  to  remember  that  —  should  not  exceed  - . 

I  =  distance  between  bracing  centres. 

r  =  least  radius  of  gyration  of  single  angle. 

L  —  total  length  of  strut. 

E  =  least  radius  of  gyration  of  combined  section. 

When  struts  of  any  section  are  hinged,  in  order  to  utilize  the 
maximum  efficiency  of  the  strut  it  is  of  the  utmost  importance 
to  keep  the  centre  of  pin  in  line  with  the  centre  of  gravity  of 
cross  section  of  the  strut.  In  the  tables  of  elements  94-101,  the 
positions  of  centres  of  gravity  are  accurately  defined. 


138 


TABLES   OF  STRUTS. 


No.  9, 
PENCOYD  ANGLES  AS  STRUTS. 

GREATEST   SAFE  LOAD  IN  LBS.  PER  SQUARE  INCH   OF   SECTION  USING 
THE   FACTORS   OF   SAFETY   OF   PREVIOUS   TABLES. 


SIZE  OP  ANGLE. 

CONDITION  OP 
ENDS. 

LENGTH  IN  FEET. 

2 

4 

6 

8 

10 

12 

14 

16 

4870 
422.1 
2930 
1690 

18 

6"x  6" 

r=  1-18 

Fixed  Ends... 
Flat  Ends  
Hinged  Ends.  .. 
Round  Ends  

14380 
14:380 
13940 
13330 

11670 
11670 
11010 
10020 

9920 
9920 
9140 
7720 

8370 
8370 
7430 
5880 

7410 
7330 
6100 
4440 

6580 
6160 
4960 
3340 

5710 
5230 
4010 
2430 

4060 
3400 
2180 
1260 

5"x5" 

r  =  -99 

Fixed  Ends  .. 
Flat  Ends  
Hinged  Ends... 
Round  Ends  — 

13840 
1:3840 
13330 
12670 

11040 
11040 
10330 
9170 

8960 
8960 
8080 
6580 

7630 
7590 
6410 
4760 

6620 
6210 
5010 
3390 

5590 
5080 
3840 
2310 

4570 
3920 
2640 
1530 

3690 
3070 
1930 
1090 

2940 
2480 
1430 
810 

4"x  4" 

r  =  -80 

Fixed  Ends  
Flat  Ends  
Hinged  En  ds... 
Round  Ends.  .  .  . 

13030 
13030 
12460 
11670 

10090 
10090 
9320 
7930 

8000 
7970 
6910 
5200 

6750 
6370 
5170 
3540 

5470 
4930 
3680 
2190 

4250 
3580 
2320 
1350 

3280 
2730 
1650 
920 

2470 
2120 
1170 
670 

1870 
1650 
890 
510 

3f'x  3f 

r  =  -69 

Fixed  Ends  
Flat  Ends     

12520 
12520 
11920 
11060 

9270 
9270 
8420 
6950 

7370 
7270 
6040 
4380 

5920 
5470 
4250 
2640 

45?,0 
'3870 
2600 
1500 

asio 

2760 
1(570 
930 

2410 
2070 
1140 
650 

1790 
1550 
830 
470 

1400 
1090 
620 
350 

Hinged  Ends.  .. 
Round  Ends  

3"x3" 

r  =  »59 

Fixed  Ends.... 
Flat  Ends  
Hinged  Ends... 
Round  Ends.  .  .  . 

11760 
11760 
11110 
10140 

8420 
8420 
7500 
5950 

6670 
6260 
5060 
3440 

5000 
4350 
3060 
1760 

3500 

2900 

2410 

2070 
1140 
650 

1720 
1460 
790 
440 

1290 
970 
580 
320 

980 
650 
420 
230 

2J"x2f" 

r  =  -64 

Fixed  Ends... 
Flat  Ends  
Hinged  Ends... 
Round  Ends  

11400 
11400 
10720 
9660 

8090 
8070 
7040 
5350 

6170 
5740 
4530 
2910 

4370 
3710 
2440 
1420 

2480 
1430 
810 

1940 
1730 
9:30 
540 

1440 
1140 
640 
360 

1040 
720 
450 
240 

780 
460 
300 
170 

2f  x2f 

T  =   -49 

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  Ends  

11040 
11040 
10830 

9170 

7680 
7640 
6470 
4830 

5630 
5130 
3900 
2350 

3760 
3K30 
1970 
1120 

2410 
2070 
1140 
650 

1630 
1350 
740 
410 

1130 
830 
510 
270 

830 
490 
320 
190 

II" 

TABLES   OF  STRUTS. 


139 


No.  9. 
PENCOYD  ANGLES  AS  STRUTS. 


A— 


— B 


</        ^ 


The  radius  of  gyration  is  taken  about  the  axis  A  B, which  also  indicates  the 
direction  of  pin  if  the  strut  is  hinged. 
r  in  marginal  columns  indicates  radius  of  gyration  around  axis  A  B. 


LENGTH  IN  FEET. 

CONDITION  OP 
ENDS. 

SIZE  OF  ANGLE. 

20 

3400 

283!) 
1730 
960 

2360 
2030 
1120 
640 

1540 
1250 
690 
380 

1070 
770 
470 
250 

740 
430 
280 
170 

22 

2780 
2360 
1340 
760 

1870 
1(550 
890 
510 

1230 
910 
550 
300 

870 
530 
350 
200 

24 

26 

28 

1660 
1390 
760 
420 

1100 
800 
490 
260 

680 
380 
240 
150 

30 

1440 
1140 
640 
360 

950 
620 
400 
220 

32 

1240 
920 
560 
300 

810 
470 
310 

180 

34 

1060 
750 
460 
240 

690 
390 
250 

150 

36 

940 
600 
390 
210 

2310 
2000 
1100 
630 

1590 
1310 
720 
400 

1000 
670 
430 
230 

690 
390 
250 
150 

1910 
1690 
910 
530 

1340 

1020 
600 
330 

820 
490 
320 
190 

Fixed  Ends... 
Flat  Ends  
Hinged  Ends... 
Round  Ends.... 

Fixed  Ends  
Flat  Ends     .... 

6"x  6" 

5"*5" 
4"x4" 
3f  x3£" 
3"x3" 

2f"x2f" 
2-1."  X2-J-" 

Hinged  Ends... 
Round  Ends  — 

Fixed  Ends  
Flat  Ends 

Hinged  Ends... 
Round  Ends  

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  Ends.... 

Fixed  Ends  — 
Flat,  Ends  
Hinged  Ends... 
Round  Ends.... 

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  Ends.... 

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  Ends  — 

I 

140 


TABLES  OF  STEUTS. 


No.  10. 
PENCOYD  ANGLES  AS  STRUTS. 

GREATEST  SAFE  LOADS  IN  LBS.  PER  SQUARE  INCH  OF  SECTION. 
(See  remarks  at  head  of  Table  No.  9.) 


CONDITION  or 

LENGTH  IN  FEET. 

ENDS. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

2J"x2f 

Fixed  Ends.... 
Flat  Ends  

10600 
10600 

7190 
7020 

5000 
4350 

3090 

2600 

187C 
165(1 

129C 
970 

89C 

55T 

640 

'  340 

.... 

•  .  . 

Hinged  Ends.. 

9860'  5800 

3060 

1530 

890 

580    360    230  .... 

r  =  -44 

Round  Ends.  .  . 

8600 

4150 

1760 

860 

510 

320 

200 

i  140 

2"x  2" 

Fixed  Ends... 
Flat  Ends 

10000 
10000 

6670 
6260 

4170 
3500 

2410 

9070 

1500 
1200 

980 
fifin 

660 

•irn 

... 

.... 

Hinged  Ends... 

9230 

5060 

2250 

1140 

670!  420'  230 

r  =  -39 

Round  Ends  

7820 

3440 

1310 

650 

370 

230 

150 

... 

If'xlf 

Fixed  Ends  
Flat  Ends 

9430 
9430 

6090 
5650 

3500 
2900 

1870 
1650 

1160 

850 

740 
430 

Hinged  Ends... 

8600 

4440 

1800 

890 

520 

28o!:;;: 

r  =  -35 

found  Ends 

7140 

2820 

1000 

510 

380 

17( 

1  1  "  V    11" 

2           •*•"» 

Fixed  Ends  
Flat  End* 

8650 
8650 

5190 
4590 

2590 
2210 

1390 

1080 

810 

480 

linged  Ends..  . 

775C 

3310 

1230 

620 

310 

T  =    '31 

iound  Ends 

6220 

194C 

700 

350 

W 

u."  x  ii" 

<Mxed  Ends  
Flat  Ends 

7860 
7830 

4000 
3340 

1750 
1500 

920 

580 

*t       ^ 

Hinged  Ends 

6720 

2130 

810 

*W) 

T==   -26 

Round  Ends 

5100 

1230 

450 

210 

Fixed  Ends 

6670 

2410 

980 

Flat  Ends 

6260 

2070 

650 

5060 

1140 

420 

r=  -20 

found  Ends.... 

3440 

650 

230 

TABLES  OF  STRUTS.  141 


TEE  STRUTS. 

The  following  tables  are  for  even  tees.  For  single  uneven  tees, 
find  the  least  radius  of  gyration  from  the  table  of  elements,  page 
101,  and  proceed  as  described  for  angle  struts,  on  page  135. 

When  a  pair  of  uneven  tees  are  braced  together  in  the  direc- 
tion of  the  shortest  leg,  they  form  a  single  strut,  whose  least 
radius  of  gyration  is  the  same  as  the  greatest  radius  of  gyration 
for  a  single  tee. 

Therefore,  when  determining  the  resistance  of  the  combined 
strut,  take  the  greatest  radius  of  gyration  from  the  table  on  page 
101,  and  the  least  radius  of  gyration,  when  determining  the  dis- 
tance between  centres  of  lateral  bracing. 

Example.— A.  pair  of  uneven  tees  5  x  2£  inches,  whose  total 
area  is  6 . 1  square  inches,  are  braced  together  in  the  direction  of 
the  shortest  leg,  forming  a  single  hinged-ended  strut  15  feet 
long.  What  is  the  greatest  safe  load,  and  what  the  greatest 
distance  between  centres  of  lateral  bracing  ? 

By  table  on  page  101,  greatest  radius  of  gyration  =  1.14  inches, 

-  =  158,  which  by  Table  No.  2  gives  3,100  Ibs.  per  square  inch, 

or  18,900  Ibs.  total  greatest  safe  load. 

Least  radius  of  gyration  =  .72,  which  multiplied  by  158  gives 
113  inches  as  the  greatest  distance  between  centres  of  lateral 
bracing. 


TABLES  OF  STBUTS. 
No.  11. 

PENCOYD  TEES  AS  STRUTS. 

GREATEST   SAFE   LOAD   IN   LBS.    PER   SQUARE   INCH   OF    SECTION. 


When  the  strut  is  free  to  fail  in  the  direction  C.  D.  Using  factors  of  safety 
given  in  previous  table. 


SIZE  OP  TEE. 

CONDITION 

OF 

ENDS. 

LENGTH  IN  FEET. 

2 

4 

6 

8 

10 

12 

14 

,,           ,, 

Fixed  Ends  

13160 

10260 

8140 

6910 

5670 

4530 

rt      •*  TC 

Fiat  Ends  

13160 

10260 

8120 

6600 

5'80 

3870!  2900 

Hinged  Ends... 

12610 

9500 

7100]     5390 

39.50 

2600 

1800 

r  =   -84 

Round  Ends  

11840 

8150 

5420     3760J     2390 

1500 

1000 

Q  1  "  v   Q  1  " 

Fixed  Ends  

12780 

9590 

7630 

6220     4910 

3660 

2710 

O^"      A  Ocj- 

Flat  Ends..   ... 

12780 

9590 

7590 

5790 

4260 

8040 

2300 

Hinged  Ends... 

12190 

8780 

6410 

4580 

2970 

1910 

1300 

r  =  -74 

Round  Ends  

11360 

7330 

4760 

2960 

1710 

1070 

740 

8"  x  f\" 

Fixed  Ends.... 

11890 

8650 

6830 

5190 

3690 

2590 

1820 

o     xs  o 

Flat  Ends  

11890 

8650 

6490 

4590 

3070 

2210 

1590 

Hinged  Knds... 

11240 

7750 

5280 

3310 

193o!   1230 

860 

r  =*  -62 

Round  Ends  — 

10290 

6220 

3650 

1940 

1090 

700 

490 

O  1  "  y   O  1  " 

Fixed  Ends... 

11400 

8090 

6170 

4370 

2940 

1930 

1440 

^^       ^    ^^ 

Flat  Ends  

11400 

8070 

5740 

3710 

2480 

1720 

1140 

Hinged  Ends... 

10720 

7040 

4530 

2440 

1430 

920 

640 

r  =   -65 

Round  Ends  

9660 

5350 

2910 

1420 

810 

540 

360 

O  1  "  X    O  1  " 

Fixed  Ends  

10770 

7410 

5270 

3370 

2070 

14:30 

990 

^47      ^   ^47 

Flat  Ends  

10770 

7330 

4680 

2800 

1830 

1120 

670 

Hinged  Ends.  .. 

10040 

6100 

3410 

1710 

990 

640 

420 

r  =  -47 

Round  Ends  

8820 

4440 

2010 

950 

570 

350 

230 

2"  x  2" 

Fixed  Ends  

10340 

6990 

4690 

2800 

1730 

1140 

790 

Flat  Ends  

10340 

6720 

4040 

2380 

1470 

840 

460 

Hinged  Ends.  .. 

9590 

5500 

2760 

1350 

790 

510 

300 

r  =  -43 

Round  Ends  

8260 

3870 

1590 

760 

440 

270 

170 

1  3"  v   13" 

Fixed  Ends... 

9590 

6220 

3660 

1980 

1250 

800 

f               47 

Flat  Ends  

9590 

5790 

3040 

1760 

930 

470 

Hinged  Ends.  .. 

8780 

4580 

1910 

950 

560 

810 

r  =  -87 

Round  Ends  

7330 

2960 

1070 

550 

300 

180 

"11"          11" 

Fixed  Ends. 

8800 

5390 

2760 

1500 

'm 

-••"'•F               •*•  ^ 

Flat  Ends..  '.  ... 

8800 

4830 

2340 

1200 

540 

Hinged  Ends.  .. 

7910 

3570 

1330 

670 

360 

r  =.  .33 

Round  Ends  — 

6400 

2120 

750 

370 

200 





TABLES  OF  STKUTS. 

No.  11. 
PENCOYD  TEES  AS  STRUTS. 

;A 


143 


'D 

Radius  of  gyration  taken  around  axis  A.  B.  which  also  indicates  the  direc- 
tion of  pin  when  strut  is  hinged,  r  in  marginal  columns  indicates  radius  of 
gyration  around  axis  A.  B. 


LENGTH  IN  FEET. 

CONDITION 

OF 

ENDS. 

SIZE  OF  TEE. 

16 

18 

20 

22 

24 

26 

28 

2660 
&*60 

1270 
730 

1980 
1760 
950 
550 

1400 
1090 
620 
350 

1040 
720 
450 
240 

700 
400 
260 
160 

2020 
1790 
970 
560 

1580 
1300 
710 
400 

1050 
730 
450 
240 

780 
4.50 
300 
170 

1650 
1380 
750 
420 

1250 
9130 
560 
300 

810 
480 
310 
180 

1350 
1030 
600 
330 

990 
670 
420 
230 

107C 

770 
470 
250 

800 
470 
310 
180 

910 

570 
370 
200 

740 

430 
280 
170 

Fixed  Ends... 
FJat  Ends  
Hinged  Ends... 
Round  Ends  

Fixed  Ends  
Flat  Ends  

4"x4" 

r  =•=   -84 

3J"  x  31" 

r  =   -74 

3"x  3" 

r  ==  -02 

21"  x  21" 

r  =  -65 

2i"x2J" 

r  =   -47 

Hinged  Ends... 
Round  Ends  

Fixed  Ends  .. 
Flat  Ends  
Hinged  Ends... 
Round  Ends  

Fixed  Ends.... 
Flat  Ends  
Hineed  Ends... 
Round  Ends  

Fixed  Ends.... 
Flat  Ends  
Hinged  Ends... 
Round  Ends.... 

SIZE  OF  TEE. 

CONDITION 
OF  ENDS. 

LENGTH  IN  FEET. 

2 

4 

6 

8 

10 

12 

14 

H"x  if 

r  =    -27 

l"x  1" 

r  =    '2« 

Fixed  Ends.... 
Flat  Ends  
Hinsred  Ends... 
Round  Ends  — 

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  Ends  

8000 
7970 
6910 
5200 

7860 
7830 
6720 
5100 

4250 
3'80 
2320 
1350 

4000 
3340 
2130 
1230 

1870 
1650 
890 
.     510 

1750 
1500 
810 
450 

1000 
670 
430 
230 

920 
580 
380 
210 

:::::: 

144 


TABLES   OF  STRUTS. 


No.  12. 
LATTICED  CHANNEL  STRUTS. 

GREATEST    SAFE    LOAD    IN   LBS.    PER    SQUARE    INCH    OF    SECTION, 
USING    FACTORS   OF   SAFETY   GIVEN   IN   PREVIOUS   TABLES.    Q 

For  a  pair  of  braced  channel?  or  for  a  single  channel  secured  from 
flexure  in  the  direction  of  the  flanges  and  liable  10  fail  only  in  the 
direction  of  the  web  C  />.  A- 

r  in  the  marginal  columns  gives  the  radius  of  gyration  for  axis 
A  B,  or  for  either  axis  of  the  combined  pair  of  channels.  See  de- 
scription, page  121. 


SIZE 

CONDITION 

LENGTH  IN  FEET. 

OP 

OF 

CHANNEL 

ENDS. 

6 

8 

10 

12 

14 

16 

18 

20 

22 

15" 

Fixed  Ends 

14110 

13570 

12900 

12400 

11890 

11400 

11040 

Flat  Ends 

14110 

1357d 

12900  12400  11890  11400 

iimn 

ia»7 

Hinged  Ends... 

..13640 

13050 

12320  11780  11240  10720  10330 

— 

Round  Ends. 

luunn 

1233,) 

11520  10900  10290    9(i(iO 

9HO 

2.05 

2.46 

2.87 

3.28   3.69 

4.10 

4.51 

12"H'y 

Fixed  Ends  

14240 

13570 

12780 

12140!11580 

11130 

10600 

10170 

Flat  Ends 

14240  13570 

12780 

12140  11580  11130 

10600 

10170 

10-3 

—      J  V      0 

Hinged  Ends.  .. 

13790  13050  12190 

115101091010420 

9860    9410 

d  —      7-5 

Round  Ends  

13160 

12330 

11360 

10600J  9900:  9290 

8600   8J40 

1.61 

2.02 

2.42 

2.83!  3.23 

3.64 

4.C4 

4.44 

12"L't 

Fixed  Ends.... 

14240 

13570 

12780 

1214011580 

11130 

10600 

10170 

r  ====     4  •  66 

Flat  Ends  

14240 

13570 

12780 

12140115801113010600 

10170 

J)  -=   10-2 

Hinged  Ends... 

1379;) 

13350 

1219:) 

11510;i0910;i0420 

9860 

9410 

d  =      7-7 

Round  Ends  



13160 

1233:) 

11360 

10600    9900    9290 

8600 

8040 

1.30 

1.62 

1.94 

2.27    2.59    2.92 

3.24 

3.16 

10"lTy 

Fixed  Ends 

1:3840 

is«nn 

12140 

11490  10950 

10430 

9920 

9430 

Flat  Ends     . 

13840  12900  12140 

11490  10950  10430 

9920 

()4;->Q 

r  =  3  "92 

Hinged  Ends 

13350  12320  11510 

10820  10230    9680 

9140 

8COO 

D=  9*° 

Round  Ends. 

, 

12670  1  ifwn  lOfino 

9780,  9050    8370 

77  -'0 

7140 

d  i==s  6  •  3 

1.71 

2.14 

2.57 

2.99   3.42   3.85 

4.28 

4.71 

10"L't 

Fixed  Ends 

13700 

12900 

12140 

11490 

10950 

10340 

9840 

9350 

Flat  Ends 

13700  12900 

12140  114UH 

10950 

10340 

9840 

9350 

r  ~^=  3  •  8  9 

D=  B'» 

Hinged  Ends... 
Round  Ends 

13200  12320 
12500J  11520 

11510 
10600 

10820 
9780 

10230 
9050 

9590 
8260 

9050 
7630 

8510 
7040 

1.42 

1.77 

2.13 

2.48 

2.84 

3.19 

3.55 

3.90 

9"He'vy 

Fixed  Ends  

14240 

13300 

12400 

11580 

10950 

10340 

9760 

9190 

8650 

r  =  3-45 

Flat  Ends  14240  13300  12400 

11580 

10950 

10340 

9760 

9190 

8(>50 

D-  8>1 
d  =  6-4 

Hinged  Ends.  ..13190,12760  11780 
Round  Ends.  ...  131(50  12000  l'»900 

10910 
9900 

10230 
9050 

9590 
8260 

8960 
7530 

83  0 
6850 

7750 
6220 

1.18    1.53 

1.97 

2.36 

2.76 

3.15 

3.55 

3.94 

4.33 

9  "Light 

Fixed  Ends.... 

14240 

13300 

12400 

11580 

10950 

10340 

9760 

9190 

8650 

7-8 

Flat  Ends  .14340,13300  12400  11580  10950 
Hinged  Ends..  .13790  12760  1178()il0910!10230 

10340 
9590 

9760 
89(50 

01  '.'0 
8330 

8H5i  1 
7750 

— 
d  =  5-  8 

Round  Ends.  .  .  .  131HO;  12000  10900 

99001  9050 

8260 

7530 

6850 

6220 

1.03 

1.38 

1.72 

2.06    2.41 

2.75 

3.10 

M, 

3.78 

TABLES   OF  STRUTS. 


145 


No.  12. 
LATTICED  CHANNEL  STRUTS. 

GREATEST   SAFE   LOAD   IN  LBS.    PER  SQUARE   INCH   OF    SECTION, 
USING  FACTORS  OF  SAFETY  GIVEN   IN   PREVIOUS  TABLES. 

The  channels  must  be  connected  so  as  to 
insure  unity  of  action  and  separated  not 
less  than  the  distances  D  or  d  respectively, 
given  in  inches  in  the  marginal  columns. 
Figures  in  heavy  type  under  each  length 
represent  the  greatest  distances  apart  in 
feet  on  each  channel  that  centres  of  lateral 
bracing  should  be  placed. 


LENGTH  IN  FEET. 

CONDITION 

SIZE 

OF 

OF 

24 

26 

28 

30 

32 

34 

36 

38 

40 

ENDS. 

CHANNEL. 

10690 

10260 

9920 

9590 

9190 

8880 

8580 

8280 

8090 

Fixed  Ends  

15" 

10690 

10260  9920  9590 

9190 

8880!  8580 

8270 

807'0 

Flat  Ends  

r  =  5.  51 

9950 

9500|  9140  8780 

8330  8000j  7670 

7300 

7040 

Hinged  Ends... 

8710 

8150  7720  7330 

6850  64901  6130 

5730 

5350 

Round  Ends  .  .  . 

D— 

4.92 

5.33 

5.74  6.15 

6.56 

6.97 

7.38 

7.79 

8.20 

9760 

9270 

8880  8500 

8230 

7950 

7720 

7500 

7240 

Fixed  Ends.... 

12"H'y 

9760 

9270 

8880  8500 

822(, 

7920 

7680 

7450 

7080 

Flat  Ends  ... 

r  =  4  -56 

8960 

8420 

8000  7580 

7240 

6840 

6530 

6220 

5860 

Hinged  Ends.. 

7530 

6950 

6490  6040 

5CGO 

5230 

4890 

4560 

4210 

Round  Ends  — 

d=  7  .  5 

4.85 

5.25 

5.66  6.06 

6.47  6.87 

7.28 

7.68 

8.09 

9760 

9270 

8880  8500 

8230 

7950 

7720 

7500 

7280 

Fixed  Ends... 

12'  Vt 

9760 

9270 

8880  8500 

8220 

7920 

7680 

7450 

7140 

Flat  Ends  

r  —  -  4.56 

8960 

8420 

8000  7580 

7240 

6840 

6530 

6220 

5920 

Hinged  Ends... 

-r\  10-2 

7530 

6950 

6490  6040 

5660 

5230 

4890 

4560 

4270 

Round  Ends  

3.89 

4.21 

4.54 

4.86 

5.19 

5.51 

5.84 

6.16 

6.49 

8960 

8420 

8140 

7860 

7590 

7320 

7070 

6830 

6580  Fixed  Ends... 

10"H'y 

8960 

8420  8120 

7830 

7540 

7210i  6840  6490 

6160  Flat  Ends... 

8080 

7500  7100 

6720 

6340 

5«>80  5620  5280 

4960  Hinged  Ends... 

D'I  -<t 

6580 

5950 

5420 

5100 

4690 

4320  3980  3650 

3340  Round  Ends.  .  . 

=  V  V 

j=r=  6-3 

6.13 

5.56 

5.99 

6.42 

6.85 

7.28 

7.71 

8.14 

8.57 

8«80 

8420 

8140 

7810 

7540 

7280 

7030 

6790 

6530 

Fixed  Ends... 

10"L't 

8880 

8420 

8120 

7780  7500 

7140  6780J  6430 

6110  Flat  Ends  

r  =^  3*  89 

8000 

7500 

7100 

6650 

6280 

5920  5560  5220 

41)10  Hineed  Ends... 

6490 

5950 

5420 

5030 

4630 

4270  3920;  S600 

3290 

Round  Ends  

d_-_—  0-3 

4.26 

4.61 

4.97 

5.32 

5.68 

6.03 

6.391  6.74 

7.10 

8280 

7950 

7630 

7320 

7030 

6750 

6440 

6130 

5840 

Fixed  Ends... 

9"He'vy 

8270 

7920 

7590 

7210 

6780 

6370  6020 

5700 

5380 

Flat  Ends  

r  =-  3  •  45 

7300 

6840  6410 

5980 

5560 

5170|  4820 

4480 

4160 

Hinged  Ends... 

5730  5230  4760 

4320  3920 

3540  !  3200 

2870 

2550 

Round  Ends  

D=  w-1 

<jr=  6  -  4 

4.73 

5.12 

5.52 

5.91 

6.30 

6.70 

7.09 

7.49 

7.88 

8230 

7900 

7590 

7280 

6990 

6710 

6400 

6090 

6800 

Fixed  Ends  

9  "Light. 

8220  7870 

7540 

7140  6720  6310  5970  5650 

5340 

Flat,  Ends  r  =  3743 

7240  678d 

6340  5920  5500  5110  4770  !  4440 

4120 

Hinged  Ends...!  ^   ,.u 

5660 

5160 

4690  4270 

3870  3490  8150  2820 

2510 

Round  Ends  

d=  6*8 

4.13 

4.47 

4.82 

5.16 

5.50 

5.85 

6.19 

6.54 

6.88 

11 


146 


TABLE  OF  STRUTS. 


NO.  13. 
LATTICED  CHANNEL  STRUTS. 

GREATEST    SAFE    LOAD    IN  LBS.    PER    SQUARE    INCH    OF    SECTION, 
USING   FACTORS  OF   SAFETY  GIVEN   IN  PREVIOUS  TABLES. 

For  a  pair  of  braced  channels  or  for  a  single  channel  secured  from 
flexure  in  the  direction  of  the  flanges  and  liable  to  fail  only  in  the 
direction  of  the  web  C  I). 

r  in  the  marginal  columns  gives  the  radius  of  gyration  for  axis 
A  JB,  or  for  either  axis  of  the  combined  pair  of  channels.  See  de- 
scription, page  121. 


SIZE 

CONDITION 

LENGTH  IN  FEET. 

OF 

OP 

CHANNEL 

ENDS. 

4 

6 

8 

10 

12 

14 

16 

18 

20 

8"He'vy 

Fixed  Ends  

13840 

12900 

11890 

11130 

10430 

9760 

9190 

8580 

Flat  Ends  

13840 

129001189011130 

10430 

9760    9190 

8580 

7-2 

Hinged  Ends... 



13350 

123201124010420 

9680 

8900    8330 

7670 

— 
d  =  4*8 

Round  Ends  .  .  . 

12670 

11520  10290 

9290 

8370 

7530;  6850 

6130 

1.39 

1.86 

2.32 

2.78 

3.25 

3.71 

4.18 

4.64 

8  "Light 

Fixed  Ends 

13970 

12900 

11890 

11130 

10520 

9810 

9190 

8580 

Flat  Ends 

13970 

12900  11890  11130 

10520 

9840'  9190 

8580 

r        3*09 

Hinged  Ends 

13500 

12320  11240 

10420 

9770 

9050    8330 

7670 

D  =  7-1 

d—  5-0 

Round  Ends 

12830 

11520  10290 

9290 

8490 

7630   6850 

6130 

1.16 

1.55 

1.94 

2.33 

2.72 

3.10   3.49 

3.88 

7"He'vy 

Fixed  Ends.... 

13430 

12270 

11310 

10520 

9760 

9040   8370 

7950 

Flat  Ends 

13430  12270  J11310  10520 

9760 

9040    8370 

7920 

6*5 

Hinged  Ends... 

12900|11650  10620 

9770 

8960 

8160    7430    6840 

rr  °   ** 

d  =  3-9 

Round  Ends  .  .  . 

*  *  *  *  ] 

12170J  10750    9530 

8490 

7530 

6670   5880 

52130 

1.46 

1.95 

2.43 

2.91 

3.40 

3.88   4.37 

4.85 

7  "Light 

Fixed  Ends 

13430 

12270 

11310 

KMSfl 

9680 

RQfifi  «aan 

7Qnn 

Flat  Ends 

13430  12270  11310  10430 

9680'  89(50    8320    7870 

r  =  2  •  64 
J)         tf  •  i 

Hinged  Ends.  .  . 

129001  11650  10620    9680 

8870    8080    7370    6780 

Round  Ends 

14170  10750    9530    8370 

7430    6580   5810    5160 

3=5      • 

1.321  1.76    2.20   2.64 

3.03   3.52,  3.96    4.40 

6"He'vy 

Fixed  Ends  

14380 

12900 

11670 

10770 

9920 

9110 

8370 

7860 

7410 

r  =  2  •  36 

Flat  Ends  14380  12900  11670  10770,  9920 

9110   8370 

7830    7*30 

D5-8 
__    m 

Hinged  Ends...  13940  12320  11010il0040i  9140 

8250    7430 

6720    6100 

d  —  3-3 

Round  Ends  ...  13330  11520  10020    8820   7720 

6760   5880 

5100 

4440 

1.14 

1.70 

2.27 

2.84   3.41 

3.98 

4.54 

5.11 

5.68 

6  "Light 

Fixed  Ends  

14240 

12900 

11580 

10690 

9760 

8880 

8180 

7720 

7240 

r  =  2-27 

Flat  Ends  

1  W40 

129001158010690 

9760    8880  '  817'0 

7680 

7080 

D=5.3 

d  =  3-5 

Hinged  Ends...  13790 
Round  Ends  ...j  13160 

12320  10910|  9950 
11520    9900    8710 

89601  8000    7170 
7530    6490    5490 

6530 
4890 

58(50 
4210 

.90 

1.351  1.80 

2.25 

2.70 

3.15    3.60 

4.05 

4.50 

5"He'vy 

Fixed  Ends  — 

13700 

12140  10860 

9840 

8800 

8090 

7500 

6990 

6490 

r  =  1  •  93 

Flat  Ends  

13700  12140  10860    9840    8800 

8070 

7450 

6720 

6070 

D4-9 

Hinged  Ends...  132001151010130    9050J  7910 

7040    6220 

5600 

4S60 

= 
d  =  2-5 

Round  Ends...  1250010600    89:J,0    7630]  6400 

5350    4560 

3870 

3240 

1.16 

1.74 

2.32   2.90   3.48 

4.06 

4.64 

5.22 

5.80 

TABLE   OF  STRUTS. 


147 


No.  13. 
LATTICED  CHANNEL  STRUTS. 

GEEATEST   SAFE  LOAD   IN  LBS.    PER  SQUARE   INCH   OF    SECTION, 

USING  FACTORS  OF  SAFETY  GIVEN  IN  PREVIOUS  TABLES. 

The  channels  must  be  connected  so  as  to 
insure  unity  of  action  and  separated  not 
less  than  the  distances  D  or  d  respectively, 
given  in  inches  in  the  marginal  columns. 
Figures  in  heavy  type  under  each  length 
represent  the  greatest  distances  apart  in 
feet  on  each  channel  that  centres  of  lateral 
bracing  should  be  placed. 


LENGTH  IN  FEET. 

CONDITION 

SIZE 

OF 

OP 

22 

24 

26 

28 

30 

32 

34 

36 

38 

ENDS. 

CHANNEL 

8140 

7770 

7410 

7070 

6750 

6440 

6090 

5750 

5430 

Fixed  Ends... 

8"He'vy 

8120 

7730 

7330 

6840   6370 

6020 

5650 

5280 

4880  Flat  Ends  

r  =   s-06 

7100 

6590 

6100 

5620 

5170 

4820 

4440   4060 

3620  Hinged  Ends... 

7.3 

5420 

4960 

4440 

3980 

3540 

3200 

2820   2470 

2150  Round  Ends  .  .  . 

— 

d  ==.  4  .  g 

5.10 

5.57 

6.03 

6.50 

6.96 

7.42 

7.89   8.35 

8.82 

8140 

7810 

7450 

7110 

6790 

6490 

6130 

5800 

5510 

Fixed  Ends... 

8  "Light. 

8120 

7780 

7390 

6900 

6430 

6070 

5700 

5340 

4980  Flat  Ends  

r  =^  3  •  09 

7100 

6650 

6160 

5680 

5220 

48<iO 

4480 

4120 

3730  Hinged  Ends... 

D7  •  1 

5420 

5030 

4500 

4030 

3600 

3240 

2870 

2510   2230  Round  Ends... 

==i    '     * 
d  ^  5.Q 

4.27 

7540 

4.66 

7190 

5.04 

6S30 

5.43 

6440 

5.82 

6050 

6.21 

5670 

6.60 

5310 

6.99    7.38 
4950    4570 

Fixed  Ends  .. 

7"He'vy 

7500 

7020 

6490 

6d20 

5610 

5180 

4730 

4300 

3920!  Flat  Ends  

6280 

5800 

5-280 

4820 

4390 

3950 

3460 

3010 

2640  Hinged  Knds... 

e-5 

4630 

4150 

3650 

3200 

2^0 

239< 

2040 

1730 

153d  Round  Ends  ... 

—    v     « 

d  =   3.9 

5.34 

5.82 

6.31 

6.79 

7.28 

7.76 

8.25 

8.73   9.22 

7500 

7110 

6750 

6350 

5960 

5500 

5190 

4820 

4450 

Fixed  Ends... 

7  '  'Light. 

7450 

6900 

6370    5930!  5520 

5C8( 

4590    4170 

3790  Flat  Ends 

6220 

5680 

5170 

4720   4300 

3840 

3310   2890 

2520  Hinged  Ends... 

D     —     «•  1 

4560 

4030 

3540 

3100    2690 

2310 

1940 

1660 

1460  Round  Ends  .  .  . 

—     w     L 

d  ==J   4  •  2 

4.84 

5.28 

5.72 

6.16    6.59 

7.03 

7.47 

7.91 

8.35 

6990 

6580 

6130 

5710   5270 

4870 

4450 

4060 

3730 

Fixed  Ends... 

6  '  '  He'vy 

6720|  6160 

5700 

5230 

4680 

4220 

3790 

3400 

3100  Flat  Ends  

r  =   2*36 

5500 

4960 

4480 

4010 

3410 

2930 

2520 

2180 

1950  Hinged  Ends... 

5.  g 

3870 

3340 

2870 

2430 

2010 

1690 

1460 

12tlO 

1100  Round  Ends... 

—    °    ° 
d  =   3,3 

6.25 

6.82 

7.38 

7.95 

8.52 

9.C9 

9.66 

10.2210.79 

6830 

6350 

5920 

5470 

5030 

4610 

4170 

3830 

3460 

Fixed  Ends... 

6  "Light. 

64  ;0 

5280 

5930   5470 
47-20   4250 

4931  » 
3680 

4390 
3110 

3960 

26HO 

3500 
2250 

3190 
2020 

2870  Flat  Ends  
1770  Hinged  Ends... 

i  =  2  -27 
D6  *  3 

3650 

3100 

2640 

2190 

1790    1550 

1310 

1150 

980,  Round  Ends  .   . 

™    °    *• 
d  —   S-6 

4.95 

5.40 

5.85 

6.30 

6.75   7.20 

7.65 

8.10 

8.55 

5920 

5430 

4910 

4410 

3930 

3530 

3150 

2780 

2500  i  Fixed  Ends... 

5"He'vy 

5470 

4880 

4260 

3750 

3280 

29-.'(» 

2640 

2360 

2140  Flat  Ends  

r  =--    i  *  93 

4250 

362*  ) 

2970 

2480 

2080 

1820 

1570 

1340 

1180  Hinged  Ends... 

D4  .  9 
—   *    v 

2640 

2150 

1710 

1440 

1190 

1010 

880 

760 

670  Round  Ends  .  .  . 

d  «=  3.5 

6.38 

6.96 

7.54 

8.12 

8.70 

9.28 

9.86 

10.44 

11.02 

148 


TABLE  OF  STRUTS. 


No.  14. 
LATTICED  CHANNEL  STRUTS. 

GREATEST    SAFE    LOAD    IN   LBS.    PER    SQUARE    INCH    OF    SECTION, 
USING   FACTORS   OF   SAFETY  GIVEN   IN  PREVIOUS   TABLES,   g 

For  a  pair  of  braced  channel?  or  for  a  single  channel  secured  from      \(\- * 
flexure  in  the  direction  of  the  flanges  and  liable  to  fail  only  in  the 
direction  of  the  web  C  D.  jf-jrl"jB 

r  in  tlie  marginal  columns  gives  the  radius  of  gyration  for  axis 
A  B,  or  for  either  axis  of  the  combined  pair  of  channels.    See  de-       h 
scrip  lion,  page  121.  L  r^ 


SIZE 

CONDITION 

LENGTH  IN  FEET. 

OP 

OP 

CHANNEL. 

ENDS. 

2 

4 

6 

8 

10 

*_ 

.*_ 

16 

18 

5" 

Fixed  Ends 

13570 

12010 

10770 

9680 

8650 

8000 

7410 

6870 

Light  .... 

Flat  Ends  

1357012010 

10770  9680 

8G50 

7970 

733H 

6550 

r  =  i-ws 

Hinged  Ends.  .. 

..'.'.'. 

13050  11380 

10040  8870 

7750 

6910 

6100  5340 

D=  4'5 

Round  Ends 

12330  10440 

8820  7430 

6220 

5200 

4440  3710 

d  =  2-8 

.96 

1.13 

1.91 

2.39 

2.87 

3.35 

3.83  4.31 

4" 

Fixed  Ends  . 

12900 

11220 

9840 

8650 

7810 

7150 

6490 

5840 

Heavy. 

Flat  Ends 

129011 

11220 

9840 

8650 

7780 

6960  6070  5380 

r  =  1  •  55 

Hiuged  Ends 

12320 

10520 

9050 

7750 

«650 

5740  4860  4160 

D  =  4'° 

Round  Ends. 

11520 

9410 

7630 

6220 

5030 

4090  3240  2550 

d  =  1-9 

1.29 

1.94 

2.53 

3.23 

3.88 

4.52  5.17 

5.81 

4" 

Fixed  Ends 

12900 

11130 

9840 

8580 

7810 

7110 

t!440 

5800 

Light  .  . 

Flat  Ends 

12900 

11130 

0840 

85SO 

7780 

6900 

6020  5340 

r&=  ^sV 
D=  3-8 

Hinged  Ends 

12320 
11520 

10420  9050  7670 
9290'  7630  6130 

6650 
5030 

5680  4820  4120 
4030  i  aannl  asm 

Round  Euds 

d  =  2  •  0 



1.25 

1.87  2.50  3.12 

3.74 

4.37 

4.99  5.62 

3" 

Fixed  Ends  

14240 

11670 

9840  8280  7370 

6490 

5590 

4780 

3960 

Flat  EIKIS  

14240 

11670 

9840 

8270  !  7270  6070 

5080 

4130 

3310 

r  =  1-18 

Hinged  Ends... 

13790 

11010 

9050 

7300  6040  i  4860 

3840 

2850 

2110 

D=3-l 

Round  Ends.  .. 

13160 

10020 

7630 

5730 

43801  3240;  2310 

1640 

1210 

d  =  1-1 

.79 

1.59 

2.38 

3.18 

3.97 

4.36 

4.76 

5.15 

5.55 

H" 

Fixed  Ends.... 

13300 

ias4o 

8180 

6950 

5750 

4610 

3560 

2730 

2090 

Flat  Ends  

13300 

10340 

8170 

6660 

5280  1  39601  2950 

28801  1840 

r  =  -85 

Hinged  Ends... 

12760 

9590 

7170 

5450 

4060  2»580 

1840 

1310 

1000 

D  =  2-4 

Round  Ends... 

12000 

8260 

5490 

3810 

2470 

1550 

1030 

740 

580 

d  =  -54 

1.01 

2.02 

3.03 

4.05 

5.06 

6.07  7.08 

8.10 

9.11 

2" 

Fixed  Ends  

12780 

9590 

7630 

6220 

4910 

3690 

2710 

1980 

1580 

Flat  Ends  

12780 

9590 

7590 

5790 

4260 

3070 

2300 

1760 

1300 

r  =  -74 

Hinged  Ends... 

12190 

8780 

6410 

4580 

2970 

1930 

1300 

950 

710 

D  =  2-l 

Round  Ends... 

11360 

7330 

47601  2960 

1710 

1090 

740 

550 

400 

d  =  -60 

.84 

1.68 

2.52 

3.35 

4.19 

5.03 

5.87 

6.70 

7.54 

TABLE   OF   STRUTS. 


149 


No.  14. 
LATTICED  CHANNEL  STRUTS. 

GREATEST   SAFE   LOAD   IX   LBS.    PER  SQUARE   INCH   OF    SECTION, 
USING   FACTORS   OF   SAFETY   GIVEN   IN   PREVIOUS   TABLES. 

The  channels  must  be  connoted  so  as  to 
insure  unity  of  action  and  separated  not 
less  than  the  distances  I)  or  d  respectively, 

fiven  in  inches  in  the  marginal  columns.      . 
'igures  in  heavy  type  under  each  length 
represent  the  greatest  distances  apart  in 
feet  on  each  channel  that  centres  of  lateral 
bracing  should  be  placed. 


LENGTH  IN  FEET. 

CONDITION 

SIZE 

OP 

OP 

20 

22 

24 

26 

28 

30 

32 

34 

36 

ENDS. 

CHANNEL. 

6310 

5800 

5270    4740 

4210 

3790 

,3370 

2970 

2640 

Fixed  Ends  

5" 

5880 

5340 

46801  4090 

3540 

3160 

2800 

2500 

2250 

Flat  Ends  

Light. 

4670 

4120 

3410i  2800 

2280 

1990 

1710 

1450 

1260 

Hinged  Ends.  .. 

r  =  1-88 

3050 

2510 

2010 

1620 

1330 

1130 

950 

820 

720 

Round  Ends  

D  =  4'5 

4.78 

5.26 

5.74 

6.22 

6.70 

7.18 

7.66 

8.14 

8.61 

d  =  2-8 

5190 

4570 

3960 

3460 

2970 

2590 

2240 

1920 

1740 

Fixed  Ends... 

4" 

4590 

3920 

,3310 

2870 

2500 

2210 

1950 

1700 

1490 

Flat  Ends  

Heavy. 

3310 
1940 

2640 
1530 

2110 
1210 

1770 
980 

1450    1230 
820      700 

1070 
610 

910 
530 

800 
450 

Hinged  Ends... 
Round  Ends  

r  =--  1  •  66 

6.46 

7.10 

7.75 

8.39 

9.04 

9.68 

10.32 

10.97 

11.61 

d  =  1-9 

5150 

4490 

3930 

3400 

2940 

2540 

2200 

1900 

1700 

Fixed  Ends... 

4" 

4540 
32fiO 

3830 

25ti() 

3280 

2080 

2830 
1730 

2480 
1430 

2170 
1210 

1920 
1050 

1680 
900 

1440  Flat  Ends  
780|HineedEnds... 

WM 

1900 

14-0 

1190 

960 

810 

690 

600 

520 

430 

Round  Ends  

D  =  3-8 

6.24 

6.86 

7.48 

8.11 

8.73 

9.35 

9.97 

10.60 

11.22 

d  =  2-0 

3280 

2680 

2220 

1850 

1610 

1390 

1180 

1020 

900 

Fixed  Ends... 

3" 

2730 

2280 

1940 

1620 

1330 

1080 

870 

700 

560  Flat  Ends  

1650 

1280 

1060 

870 

730 

620 

530 

440 

370  Hinged  Ends... 

r  =  1-18 

920!     730!     610 

500 

410 

350 

280 

230 

200;  Round  Ends  ... 

D=3-l 

7.94 

8.33 

8.72 

9.12 

9.51 

11.90 

12.29 

12.69 

13.08 

d  =  1-1 

1690 
1430 

1380 
106U 

1100 

800 

930 

600 

770 
450 

Fixed  Ends.... 
Flat  Ends... 

2V 



770 

610 

490 

390 

5>90 

.  Hinged  Ends... 

r  =   -85 

430 

340 

260 

210      170 

Round  Ends. 

D  =  2-4 

10.12 

11  13 

12  14  13  Ifi  14  17 

d  =   -64 

1250 

990 

800 

FiTod  "Ends 

2" 

930 

670 

470 

Flat  Ends  

560 

420 

310 

Hinged  Ends... 

r  =  -74 

300 

230 

180 

Round  Ends. 

T)  =  2  "  * 

8.38 

9.22 

10.05 

d  =      80 

150  TABLES  OF  STRUTS. 

No.  15. 
PENCOYD  CHANNELS  AS  STRUTS. 

GREATEST  SAFE  LOADS  IN  LBS.  PER  SQ.  INCH  OF  SECTION,  WHEN  THE 
STRUTS  ARE  FREE  TO  BEND  AT  RIGHT  ANGLES  TO  THE  WEB  OR  IN 
THE  WEAKEST  DIRECTION,  USISG  FACTORS  OF  SAFETY  GIVEN  IN 
PREVIOUS  TABLES. 


SIZE 

OP 

CHANNEL 

CONDITION 

OF 

ENDS. 

LENGTH  IN  FEET. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

1  V 

Fixed  Ends.... 

14240 

11580 

9680 

8180 

7240 

6350 

5430 

4570 

3790 

S-O 

Flat  Ends  

14240 

11580   9680 

8170 

7080 

5930 

4880 

3920 

3160 

Hinged  Ends..  . 

13790 

10910    8870 

7170 

5S60 

4720 

3620 

2640 

1990 

T  =    1-13 

Round  Ends  

13160 

9900 

7430    5490 

4210 

3100 

2150 

1530 

1130 

1  0" 

Fixed  Ends  

13570 

10690 

8580    7320 

6220 

5110 

4060 

3220 

2520 

LA 

Flat  Ends  

13570 

10690 

8580    7210    5790 

4490 

3400 

2690 

2160 

Heavy  

I  =      -92 

Hinged  Ends... 
Round  Ends  

13050 
12330 

9950 
8710 

7670    5980    4580 
6130   4320   2960 

3210 
4860 

2180 
1260 

1610 
900 

1200 
680 

10" 

Fixed  Ends... 

12780 

9590 

7630    6220    4910 

3660 

2710 

1980 

1580 

1  — 

Flat  Ends            12780 

9590 

7590   5790    4260 

3040 

2300 

1760 

1300 

Light  

I  =      -74 

Hinged  Ends... 
Round  Ends.  .  .  . 

12190 
11360 

8750 
7330 

6410 
4760 

4580 
2960 

2970 
1710 

1910 
1070 

1300 
740 

950 
550 

710 
400 

1  0" 

Fixed  Ends... 

13160 

10260 

8140 

6910 

5670 

4530 

3500 

2660 

2020 

1U 

Flat  Ends  

13160 

10260 

8120 

6600 

5180!  3870 

2900 

2260 

1790 

Heavy.  .  .  . 

Hinged  Ends... 

12610 

9500 

7100 

5390 

3950'  2600 

1800 

1270 

970 

r  =     -84 

Round  End*.  .  .  . 

11840 

8150 

5420 

3760 

2390 

1500 

1000 

720 

560 

10" 

Fixed  Ends  

12400 

9190 

7320 

5840 

4410 

3220 

2340 

1740 

1360 

1U 

Flat  Ends  1->400 

9190 

7210 

5380 

3750    2690 

2020 

1490 

1040 

Light  

r  =      -69 

Hinged  Ends... 
Round  Ends  

11780 
10900 

8330 
6850 

5980 
4320 

4160 
2550 

2480 
1440 

1610 
900 

1110 
630 

800 
450 

600 
340 

Q" 

Fixed  Ends  

12400 

9110 

7240 

5750 

4330 

3120 

2240 

1690 

1320 

y 

Flat  Ends  !  12400 

9110 

7080 

5280 

3K60 

2620 

1950 

1430    1000 

Heavy  

Hinged  Ends... 

11780 

8250 

5860 

4060 

2400 

1550 

1U70 

7',0|     590 

r  -=     -6S 

Round  Ends  

10900 

6760 

4210 

2470 

1390 

870 

610 

430 

320 

Q" 

Fixed  Ends  

11670 

8370 

6620 

4910 

3400 

2310 

1660 

1240 

940 

V 

Flat  Ends  

11670 

8370 

081*. 

4260 

2830 

2000 

1390 

920 

600 

Light  

Hinged  Ends... 

11010 

74:30 

5010 

2970 

1731 

1100 

760 

560 

390 

r=     -6» 

Round  Ends  

10080 

5880 

3390 

1710 

960 

630 

420 

300 

210 

TABLES  OF  STKUTS. 


151 


No.  15. 


PENCOYD  CHANNELS  AS  STRUTS. 

T.  JU 


r  in  marginal  columns  is  the  radius  of  gyration  taken  around  axis  A  B. 
When  strut  is  hinged  the  pins  are  supposed  to  lie  in  the  direction  A  B. 
When  the  pins  are  in  the  direction  (J D,  consider  the  strut  flat  ended  by 
tliis  table. 


LENGTH  IN  FEET. 

CONDITION 

OP 

ENDS. 

SIZE 

OF 

CHANNEL. 

20 

22 

24 

26 

28 

30 

32 

34 

£6 

3120 
26211 
1550 
870 

1940 
1730 
930 
540 

1250 
930 
560 
300 

1650 
1380 
750 
420 

1050 
73f 
450 
240 

1020 
690 
440 
230 

710 
400 
260 
160 

2540 
2170 
1210 
690 

1640 
1360 
740 
410 

990 
670 
420 
230 

1350 
1030 
600 
330 

830 
490 
330 
190 

810 
470 
310 
180 

2070 
1830 
990 
570 

1360 
1040 
600 
340 

800 
470 
310 
180 

1070 
770 
470 
250 

670 
370 
240 
150 

1760 
1520 
820 
460 

1100 
800 
490 
260 

1520 
1220 
680 
370 

950 
610 
400 
210 

1300 
980 
580 
320 

790 
4fiO 
300 
170 

1090 
800 
490 
260 

970 
640 
410 
220 

840 
500 
330 
190 

Fixed  Ends  
Flat  Ends  
Hinged  Ends.  .. 
Round  Ends  .  .  . 

Fixed  End?  
Flat  Ends  
Hinged  Ends... 
Round  Ends  

Fixed  Ends.... 
Flat  Ends  
Hinged  Ends... 
Round  Ends  

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  Ends  — 

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  Ends  

Fixed  Ends  — 
Flat  Ends  
Hinged  Ends.  .. 
Round  Ends.... 

Fixed  Ends  
Flat  Ends.    .   .. 
Hinged  Ends... 
Round  Ends  

15" 

r  =  1-13 

12" 

Heavy. 

12" 

Light. 

r  —      -74 

10" 

Heavy. 
10" 

rW;, 
9" 

Heavy. 

r  —      -68 

9" 

Light. 

r~  -      '60 





910 

570 
370 
200 

740 
430 
280 
170 

l 

I 

[::::: 

I  

152  TABLES   OF   STRUTS. 

No.  16. 
PENCOYD  CHANNELS  AS  STRUTS. 

GREATEST  SAFE  LOAD  IN  LBS.  PER  SQ.  INCH  OF  SECTION  WHEN  THE 
STRUTS  ARE  FKEE  TO  BEND  AT  RIGHT  ANGLES  TO  THE  WEB  OR 
IN  THE  WEAKEST  DIRECTION,  USING  FACTORS  OF  SAFETY  GIVEN 
IN  PREVIOUS  TABLES. 


SIZE 

OF 

CHANNEL 

CONDITION 

OF 

ENDS. 

LENGTH  IN  FEET. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

Q" 

Fixed  Ends... 

12520 

9350 

7450 

6010 

4610 

3400 

2470 

1840 

1450 

o 

Flat  Ends  

12520!  9350 

7390 

5.560 

3960 

2830 

2120 

1610 

1150 

Heavy.  .  . 

Hinged  Ends.  .. 

11920:  8510 

6160 

4350 

2680 

1730 

1170 

870 

650 

r  =   -71 

Round  Ends  .  .  . 

11060 

7040 

4500 

273U 

1550 

960 

670 

50C 

360 

Q" 

Fixed  Ends  

11760 

8420 

6670 

5000 

3500 

2410 

1720 

1290 

980 

O 

Flat  Ends  

117'60 

8420 

6260 

4350 

2900 

2070 

1460 

970 

650 

Light.... 

r  =   -60 

Hinged  Ends... 
Uoinul  Ends  .  .  . 

11110 
10140 

7500 
5950 

5060 
3440 

3069 
1760 

1800 
1000 

1140 
650 

790 
440 

580 
320 

420 
230 

7" 

Fixed  Ends  

12140 

8880 

7030 

5470 

4000 

2830 

2000 

1550 

1170 

I 

Flat  Ends 

12140 

8880 

6780 

4930 

3340 

2400 

J780 

1260 

860 

Heavy  

Hinged  Ends... 

11510 

8000 

5560 

3680 

2130 

1370 

960 

700 

530 

r  =   -66 

Round  Ends  — 

10600 

6490 

3920 

2190 

1230 

770 

560 

.  390 

280 

7" 

Fixed  Ends.... 

11670 

8280 

6490 

4780 

3280 

2220 

1610 

1180 

900 

i 

Flat  Ends  

11670|  8270 

6070 

4130 

2730 

1940 

1330 

870 

560 

Light  

[linged  Ends.  .. 

11010 

7300 

4860 

2850 

1650 

1060 

730 

530 

370 

r  =  -5S 

Round  Ends  .  .  . 

10020 

5730 

3240 

1640 

920 

610 

410 

280 

200 

fi" 

?ixed  Ends  

12270 

9040 

7190 

5670 

4210 

3030 

2150 

1640 

1270 

u 

?lat  Ends  

12270 

9040 

7020 

5180 

3540 

2550 

1890 

1360 

950 

Heavy  — 

linged  Ends... 

11650 

8160 

5800 

3!  »50 

2280 

1490 

1030 

740 

570 

r  =  -«7 

lound  Ends  .  .  . 

10750 

6670 

4150 

2390 

1330 

840 

590 

410 

310 

fi" 

Hxed  Ends.  .. 

11130 

7770 

5750 

3890 

2520 

1690 

1200     870 

Flat  Ends. 

11130 

7730 

5280 

3250 

2160 

1430 

880 

530 

Light.... 

r  -=   -51 

Hinged  Ends... 
Round  Ends  .  .  . 

10420 
9290 

6590 
4960 

401)0 
2470 

2060 
1180 

1-200 
680 

770 
4:30 

540 
290 

350 
200 

K" 

Fixed  Ends... 

11490 

8140 

6260 

4530 

3060 

2020 

1500 

1070 

820 

u 

Flat  Ends  

114«K) 

8120 

5830 

3870 

2570 

1790 

1200 

770 

480 

Heavy  

Hinged  Ends... 

10820 

7100 

4620 

2600 

1510 

970 

670 

470 

320 

r  =  -5« 

Round  Ends  .  .  . 

9780 

5420 

3000 

1500 

850 

560 

370 

250 

180 

TABLES  OF  STRUTS. 

No.  16. 
PENCOYD  CHANNELS  AS  STRUTS. 


153 


r,  in  marginal  columns,  is  the  radius  of  gyration  taken  around  axis  A  B. 
When  strut  is  hinged,  the  pins  are  supposed  to  lie  in  the  direction  A  B. 
When  the  pins  are  in  the  direction  CD,  consider  the  strut  flat  ended  by  this 
tuble. 


SIZE 

CONDITION 

LENGTH  IN  FEET. 

OP 

OP 

CHANNEL 

ENDS. 

2 

4 

6 

8 

10 

12 

14 

16 

18 

K" 

Fixed  Ends  

10600 

7190 

5000 

3090 

1870 

1290 

890 

0 

Flat  Ends  10600 

7020 

4350 

2600 

1650 

970 

550 

Light.... 

r  =  -45 

Hinged  E.ids..  . 
Round  Ends  .  .  . 

9860 
8(500 

5800 
4150 

3060 
1760 

1530 
860 

890 
510 

580 
320 

3GO 
200 

A" 

Fixed  Ends  ... 

11040 

7080 

5630 

3760 

2410 

1630 

1130 

830 

rr 

Flat  Ends  

11040 

7640 

5130 

3130 

2070 

1350 

8:30 

490 

Heavy.  .  . 

Hinged  Ends..  . 

10330 

6470 

3900 

1970 

1140 

740 

510 

320 

r  =  -50 

Round  Ends  .  .  . 

9170 

2350 

1120 

650 

410 

270 

190 



A" 

Fixed  Ends  

10860 

7500 

5390 

3500 

2180 

1500 

1040 

740 

4: 

Flat  Ends  

10860 

7450 

4830 

2900 

1910 

1200 

720 

430 

Light  .... 

Hinged  Ends.  .  . 

10130 

6220 

3570 

1800 

1040 

670 

450 

280|  

r  =  -4b 

Round  Ends  .  .  . 

8930 

4560 

2120 

1000 

600 

370 

240 

170 



0" 

Fixed  Ends  

10690 

7320 

5110 

3220 

1940 

1360 

950 

670 

o 

Flat  Ends  

10690 

7210 

4490 

2690 

1730 

1040 

610 

370 

Hinged  Ends  .  . 

9950 

5980 

3210 

1610 

930 

600 

400 

240 

'.  '.  '.  '.  '. 

r  =  -46 

Round  Ends  .  .  . 

8710 

4320 

1860 

900 

540 

340 

220 

150 



91" 

Fixed  Ends  

10340 

6990 

4690 

2800 

1730 

1140 

790 

"4" 

Flat  Ends  

10340 

6720 

4040 

2380 

1470 

840 

460 

... 

Hinged  Ends..  . 

9590 

5500 

2760 

1350 

790 

510 

300 

r  =  -43 

Round  Ends 

8260 

3870 

1590 

760 

440 

270 

170 

O" 

Fixed  Ends. 

8650 

5190 

2'90 

1390 

810 

2 

Flat  Ends 

8650 

4590 

2210 

1080 

480 

Hinged  Ends  !  . 

7750 

3310 

1230 

62*. 

310 

r  =  -31 

Round  Ends  .  .  . 

6220 

1940 

700 

350 

180 

154  TABLES   OF  STKUTS. 

WROUGHT  IRON  COLUMNS  OR  PILLARS  OF  ROUND 
AND  SQUARE  CROSS  SECTION. 

Experiments  on  columns  of  this  class  are  not  very  complete, 
especially  as  denoting  the  comparative  values  for  the  various  end 
conditions.  The  following  tables,  Nos.  17  and  18,  are  derived 
partly  from  experiment  on  actual  columns,  extended  and  com- 
pleted by  comparison  with  the  experiments  on  rolled  struts 
from  which  all  our  previous  tables  of  strut  resistances  are  derived. 

Table  No.  2  is  taken  as  the  basis  for  the  working  values.  On 
account  of  the  more  perfect  symmetry  of  form  possessed  by  round 
and  square  sections  than  the  shapes  for  which  table  No.  2  was 
especially  calculated,  the  safe  loads  per  square  inch  of  section 
are  increased  ten  (10)  per  cent,  for  round  columns,  and  five  (5) 
per  cent,  for  square  columns.  That  is,  the  factors  of  safety  pre- 
viously given  remaining  the  same,  the  ultimate  strength  is  sup- 
posed to  be  10  and  5  per  cent,  respectively  greater  than  the 
rolled  struts. 

The  tables  are  calculated  for  certain  thicknesses  of  iron  vary- 
ing from  •§"  for  2"  diameter  up  to  £"  for  12"  diameter,  as 
marked  in  the  margins.  At  the  same  place  R  represents 
the  radius  of  gyration  for  the  diameter  and  thickness  given. 
When  the  thickness  varies  but  a  little  from  that  given,  the 
strength  per  square  inch  of  section  can  be  accepted  as  practically 
unchanged.  But  when  the  variation  becomes  of  importance, 
the  radius  of  gyration  corresponding  to  the  altered  thickness 
will  have  to  be  obtained,  and  the  strength  of  the  column  then 
ascertained  from  table  No.  2,  as  heretofore  described. 

The  following  table  gives  the  values  of  the  radius  of  gyration 
for  round  and  square  columns  from  2  to  12  inches  diameter,  and 
.from  ^0  of  an  inch  to  1  inch  thick. 

Example  for  Round  Column  : 

What  is  the  greatest  safe  load  for  a  flat-ended  round  column 
6  inches  outer  diameter,  |"  thick,  8.64  sq.  in.  area,  and  18  feet 

long,     r^l.95    -  =111.     By  table  No.  2  the  corresponding 

safe  load  =  6780  Ibs.  +  10  per  cent.  =  7460  Ibs.  per  sq.  inch  of 
section,  or  64,440  Ibs.  for  the  column. 

For  a  square  column  add  5  per  cent,  to  table  No.  2,  instead  of 
10  per  cent,  as  above. 


TABLES  OF  STKUTS. 


155 


RADII  OF  GYRATION  FOR  ROUND  COLUMNS. 


THICKNESS  IN  INCHES  VARYING  BY  TENTHS. 

OUTSIDE 
DIAMETER 

.2 

.3 

.5 

.6 

.7 

.8 

.9 

1.0 

OP  COLUMN 

IN  INCHES. 

CORRESPONDING  RADIUS  OP  GYRATION  IN  INCHES. 

2 

.67 

.64 

.61 

.58 

.56 

.54 

.52 

.51 

.50 

.50 

3 

1.03 

.99 

.96 

.93 

.90 

.88 

.85 

.83 

.81 

.79 

4 

1.38 

1.35 

1.31 

1.28 

1.45 

1.22 

1.19 

1.16 

1.14 

1.12 

5 

1.73 

1.70 

1.66 

1.63 

1.6D 

1.57 

1.54 

1.51 

1.48 

1.46 

6 

2.08 

2.05 

2.02 

1.98 

1.95 

1.92 

1.89 

1.86 

1.83 

1.80 

7 

2.43 

2.40 

2.36 

2.33 

2,30 

2.27 

2.24 

2.21  . 

2.18 

2.15 

8 

2.79 

2.76 

2.72 

2.69 

2.66 

2.62 

2  59 

2.56 

2.53 

2.50 

9 

3.15 

3.11 

3.08 

3.04 

3.01 

2.97 

2.94 

2.91 

2.882.85 

10 

3.51 

3.47 

3.44 

3.40 

3.37 

3.33 

3.3J 

3.27 

3.23 

3.20 

11 

3.86 

3.82 

3.79 

3.75 

3.72 

3.68 

3.65 

3.62 

3.583.55 

12 

4.21 

4.18 

4.15 

4.11 

4.08 

4.04 

4.01 

3.97 

3.94 

3.90 

RADII  OF  GYRATION  FOR  SQUARE  COLUMNS. 


OUTER 


THICKNESS  IN  INCHES  VARYING  BY  TENTHS. 


DIAMETER 

ACROSS 

.1 

.2 

3 

.4 

.5 

.6 

.7 

.8          .9 

1.0 

FLATS  IN 

INCHES. 

CORRESPONDING  RADIUS  OP  GYRATION  IN  INCHES. 

2 

.78 

.74 

.71 

.68 

.65 

.63 

.61 

.59 

.58 

.58 

3 

1.18 

1.14 

1.11 

1.08 

1.04 

1.01 

.98 

.96 

.93 

.91 

4 

1.59 

1.55 

1.51 

1.47 

1.44 

1  41 

1.38 

1.35 

1.32 

1.29 

5 

2.00 

1.96 

1.92 

1.89 

1.85 

1  81 

1.78 

1.75 

1.71 

1.68 

6 

2.41 

2.37 

2.33 

2.29 

2.25 

2.21 

2.18 

2.15 

2.11 

2.08 

7 

2  82 

2.78 

2.74 

2.70 

2.66 

2.62 

2.58 

2.55 

2.51 

2.48 

8 

3.  -23 

3.19 

3.15 

3.11 

3.07 

3.03 

2.9'.t 

2.96 

2.92 

2.89 

9 

3.63 

3  59 

3.55 

3.51 

3.48 

3.44 

3  40 

3.36 

3.32 

3  29 

10 

4.04 

4.00 

3.96 

3.92 

3.88 

3.84 

3.80 

3.77 

3.73 

3.70 

11 

4.45 

4.41 

4.37 

4.33 

4.29 

4.25 

4.21 

4.17 

4.13 

4.10 

12 

4.86 

4.82 

4.78 

4.74 

4.70 

4.66 

4.62 

4.58 

4.544.51 

156 


TABLES   OF  STRUTS. 


No.  17. 
ROUND  COLUMNS. 

GREATEST   SAFE   LOADS  IN  LBS.    PER  SQ.    IN.    OF  SECTION. 


By  this  table  for  the  same  ratios  of  -  the  safe  loads  are  increased  10  per 
cent,  over  the  results  obtained  for  previous  tables,  as  given  in  table  No.  2. 


SIZE 

OUTKU 

DIAME- 
TER. 

CONDITION 

OF 

ENDS. 

LENGTH  IN  FEET. 

2 

4 

6 

8 

10 

12 

13350 
13350 
12670 
11660 

12640 
12640 
12000 
10890 

11570 
11570 
10740 
9330 

9940 
9940 
8970 
7330 

8840 
8820 
7660 
5790 

7860 
7050 
6310 
4490 

6190 
5640 
4290 

2580 

3230 
2720 
1570 
890 

14 

16 

18 

12" 

Diameter. 
1"  thick.. 

R=3-»4 

10" 

Diameter, 
i"  thick.. 

R  =  3-37 

8" 

Diameter. 

i"  thick.. 

R  =  2-8« 

6" 

Diameter. 
f  '  thick.. 

R=2-00 

5" 

Diameter, 
f"  thick  . 
R  =  i-«4 

4" 

Diameter. 
J"  thick.. 

R^l  33 

3" 

Diameter. 
W  thick. 
R  =  i-oo 

2" 
Diameter 
I"  thick.. 
ll=-«« 

Fixed  Ends  

15220 
15220 
14680 
13940 

14630 
14630 
140:30 
13200 

13490 
13490 
12810 
11820 

12140 
12140 
113(50 
10080 

11090 
11090 
10250 
8720 

9940 
9940 
8970 
7330 

8440 
8400 
7110 
5310 

6140 

5f>80 
4220 
2540 

14.330 
14330 
13700 
12840 

13490 
13490 
12810 
11820 

12440 
12440 
11680 
10480 

11000 
11000 
10150 
8600 

9850 
9850 
8880 
7230 

8740 
8710 
7520 
5750 

7330 

6880 
5560 
3780 

4510 
37^0 
2420 
1390 

12640 
12640 
12000 
10890 

11940 
11940 
11140 
9820 

10730 
10730 
9850 
8-280 

9050 
9040 
7960 
6220 

8150 
8060 
6710 
4880 

7040 
6560 
5240 
3460 

5110 
4400 
2990 
1720 

2290 
2020 
1100 
630 

12040 
12040 
11250 
9950 

11280 
11280 
10450 
8960 

9940 
9940 
8970 
7330 

8440 
8400 
7110 
5310 

7460 
7260 
5920 
4130 

6190 
5640 
4290 
2580 

41:30 
3440 
2160 

1230 

17IX) 
1440 
790 
440 

11470 
11470 
10840 
9200 

10640 
10640 
9750 
8170 

9200 
9200 
8170 
6460 

7860 
7650 
6310 
4490 

6740 
6270 
4920 
3150 

5400 
4680 
3260 

1880 

3300 
2780 
1610 
910 

1340 
990 
600 
330 

Flat  Ends  
Hinged  Ends..  . 

Round  Ends  

Fixed  Ends  
Flat  Ends 



.... 

15660 
15660 
15160 
14470 

14770 
14770 
14190 
13380 

13490 
13490 
12810 
11820 

12540 
12540 
11790 
10620 

11570 
11570 
10740 
9330 

9940 
9940 
8970 
7330 

7820 
7590 
6240 
4430 

Hinged  Ends... 
Round  Ends.  .  . 

Fixed  Ends  

Flat  Ends 

Hinged  Ends.. 

Round  Ends. 

Fixed  Ends  
Flat  Ends  
Hinged  Ends  . 

15220 

15220 
14680 
13940 

14470 
14470 
13870 
13020 

13490 
13490 
12810 
11820 

12140 
12140 
11360 
10080 

9850 
98.50 
8880 
7230 

Round  Ends. 

Fixed  Ends  
Fhit  Ends  

Kin  ired  Ends... 
Round  Ends  

Fixed  Ends  
Flat  Ends  
Hinged  Ends 



Round  Ends  

Fixed  Ends  
Flat  Ends  
Hinged  Ends  .  , 
Round  Ends.  .  . 

Fixed  Ends.  .. 
Flat  Ends..  .. 
Hinged  Ends*  .  . 
Round  Ends.  .  . 

15220 

15220 
14680 
13940 

13490 
13490 
12810 
11820 

TABLES   OF  STRUTS.  157 

No.  17. 
ROUND  COLUMNS. 

GREATEST   SAFE   LOADS   IN   LBS.    PER   SQ.  IN.    OF   SECTION. 

The  calculations  are  based  on  the  thicknesses  and  radii  of  gyration  marked 
under  the  diameters  on  marginal  columns.    See  description. 


LENGTH  IN  FEET. 

CONDITION 

OP 

ENDS. 

SIZE 
OUTER 
DIAME- 
TER. 

20 

22 

24 

26 

28 

30 

32 

34 

36 

10910 

10370 

9850 

9350 

8990 

8640 

8340 

8050 

7770 

Fixed  Ends  

12" 

10910103701  9850    9350 

8980 

8610 

8290 

79HO 

7520 

Flat  Ends  

Diameter. 

10050 
8490 

9-160    8880    8330 
7850)  7230  !  6640 

7880 
6030 

7390 
5610 

6970 
5150 

6570 
4750 

6180 
4370 

Hinged  t  nds..  . 
Round  Ends  

|"  thick. 

R  —  3-94 

10020 

9430 

8990 

8620 

8:50 

7910 

76CO 

7280 

6940 

Fixed  Ends... 

10" 

10020 

9430 

8980 

8610 

8190 

7720 

7260   6830 

6460  Flat  Ends  Diameter. 

9070 

8430 

78SO 

7390 

6840 

6380 

6980 

5510 

5130!Hinged  Ends.  .  .    *"  thick. 

7430 

6740 

6030 

5610 

5010 

4560 

4130 

3730 

3350 

Round  Ends  

R  =  3'37 

811 

8740 

8290 

7860 

7460 

7040 

6610 

6190 

5790 

5400 

Fixed  Ends... 

8710 

8250 

r.650 

7070 

6560 

6110 

5640 

5140 

4680  Flat  Ends  Diameter. 

7520 
5750 

6900 
5090 

6310 
4490 

5920 
3960 

5240 
3460 

4780 
3000 

4290 
2580 

3750 
2210 

3260  Hinged  Ends... 
1880  1  Round  Ends  

i"  thick. 

XV  ~  ^  '  °** 

7330 

6740 

6190 

5660 

5110 

4580 

4130 

3700 

3300'Fixed  Ends... 

6" 

6880 

6:70    5640 

4990 

4400 

3850 

3440 

3C80i  2780  Flat  Ends  Difimeter. 

5560 
3780 

4920 
3150 

4290 
2580 

3580 
2090 

2990 
1720 

2470 
1440 

2160 
1230 

1880 
1C40 

161()iHiiigedEids... 
910.Round  Ends  

|    thick. 
R  =  a-uo 

6100 

5440 

4760 

4210 

3670 

3160 

2^90 

2420 

2110!Fixed  Ends  

5" 

55301  47301  4020 

3500 

3050 

2680 

2380 

2110 

1870!Flat  Ends  Diameter. 

4160 
2490 

33101  2640 
1900    1520 

2220 
1260 

1850 
1030 

1540 
860 

1330 
750 

1150 
660 

1000 

580 

H  nged  Ends... 
Round  Ends  

StfRft 

4580 

3880   3260 

2770 

2320 

2000 

1780 

1560 

1360 

Fixed  Ends...  . 

4" 

3850 

3210 

2750 

2370 

2040 

1740 

1470 

1220 

1010 

Flat  Ends  

Diameter. 

2470 
1440 

2000 
1110 

1590 
900 

13:0 
740 

1110 
630 

940 
530 

800 
450 

690 
380 

610 
330 

Hinged  Ends... 
Round  Ends.  .  .  . 

i"  thick. 

R=  i'33 

2650 

2100 

1790 

1500 

1240 

1070 

910 

770 

Fixed  Ends.... 

3" 

2270 

1850 

1480 

1150 

910 

710 

530 

440 

Flat  Ends  

Diameter. 

1250 

1000     810 

670 

560 

460      3.50 

2801  .., 

Hinged  Ei  els..  . 

-fa"  thick. 

710 

580 

450 

370 

290 

2501     200 

170 

Round  Ends  

R=i-oo 

1040 

810 

Fixed  Ends..  .. 

9" 

*"* 

680 

470 

Flnt  Ends  

440      300 
240     180 

1 

Hinged  Ends... 
Round  Ends..  .  . 

Dintn^tcr. 
t"  thick. 

T?  _   •  66 

1 

J\  — 

158 


TABLES  OF  STEUTS. 


No.  18. 
SQUARE  COLUMNS. 

GREATEST   SAFE  LOAD   IN  LBS.    PER  SQUARE   INCH   OF   SECTION. 

By  this  table  for  the  same  ratios  of  — ,  the  safe  loads  are  increased  5  per 
cent,  over  the  results  obtained  in  table  No.  2. 


SIZE 

OF 

COLUMN. 

CONDITION 

OP 

ENDS. 

LENGTH  IN  FEET. 

2 

4 

10330 
10330 
9500 
8010 

12160 
12160 
11460 
10400 

13540 
13540 
12940 
12100 

14390 
14390 
13860 
13120 

14950 
14950 
14480 
13820 

6 

8 

6760 
6320 
5060 
3360 

8690 
8680 
7660 
6020 

10330 
10330 
9500 
8010 

11310 
11310 
10540 
9260 

12160 
12160 
1  1460 
10390 

13540 
13540 
12940 
12100 

14380 
14380 
13S60 
13120 

14950 
14950 
14480 
13820 

10 

12 

14 

16 

18 

2" 

i"  thick.. 
R  =  •« 

3" 

^thick 

4" 

}"  thick.. 

R=  1-53 

5" 

t"  thick.. 

R  =  !•«» 

6" 

t"  thick.. 

.R=2-30 

8" 

J"  thick.. 

R  =  3-07 

10" 

i"  thick.. 

R=3-«7 

12" 

4"  thick.. 

R  =  4-56 

Fixed  Ends.... 
Flat  Ends 

13540 
13540 
12910 
12100 

14950 
14950 
14480 
13810 

8160 
8120 
6920 
5210 

10330 
10330 
9500 
8010 

11690 
11690 
10940 
9750 

12610 
12610 
11950 
10960 

13540 
13540 
12940 
12100 

14670 
14670 
14170 
13470 

5410 
4770 
3420 
2000 

7690 
7570 
6280 
4540 

9010 
9010 
8050 
6440 

10250 
10250 
9410 
7910 

11220 
1122G 
10450 
9150 

12480 
12480 
11800 
10800 

13540 
13>40 
12940 
12100 

14250 
14250 
13700 
12950 

4130 

i  3440 
2180 
1250 

6760 
6323 
5060 
3360 

8150 
8HO 
6920 
5210 

9170 
9170 
8220 
66:30 

10330 
10330 
9500 
8010 

11690 
11690 
10940 
9750 

12750 
12750 
12090 
11130 

13420 
13420 
12800 
11930 

3090 
2600 
1500 
850 

5830 
5280 
3980 
2380 

7420 
7180 
5900 
4180 

8400 
8370 
7260 
5460 

9410 
9410 
84*0 
6910 

10950 
10950 
10160 
8790 

12060 
2060 
1360 
10270 

2750 
2750 
12090 
11130 

2310 
2020 
1100 
630 

4920 

4240 
2900 
1680 

6720 
6220 
5010 
3310 

7780 
7700 
6400 
4660 

8690 
8680 
7660 
6020 

10250 
10250 
9410 
8010 

11400 
11400 
10(540 
9380 

12140 
12140 
11460 
10400 

1790 
1510 
820 
450 

4080 
3410 
2160 
1240 

6040 
5540 
4260 
2590 

7260 
6930 
5660 
3950 

8160 
8120 
6920 
5210 

9650 
9650 
8750 
7190 

10860 
10860 
10070 
8670 

11690 
116M) 
10940 
9750 

Hinged  Ends... 
Round  Ends  

Fixed  Ends  
Flat  Ends  
Hinged  Ends... 
Round  End*  

Fixed  Ends 

Flat  Ends  . 

Hinged  Ends..  . 
Round  End* 

Fixed  Ends 

Flat  Ends  
Hinged  Ends.  .. 
Round  Ends 



Fixed  Ends 

Flat  Ends  
Hinged  Knds 



Round  Ends 

Fixed  Ends 

Flat  Ends.  .. 

rlinged  Ends 

Round  Ends.  . 

Fixed  Ends  ... 

Flat  Ends 

Hinged  Ends... 

Round  Ends  

Fixed  Ends.... 

Flat  Ends 

Hinge<  1  Ends.  .. 

Round  Ends.  .  . 

TABLES   OF  STR 

No.  18. 
SQUARE  COLUM 

GREATEST  SAFE  LOAD  IN  LBS.  PER  SQUARE 

The  calculations  are  based  on  the  thicknesses  and  radii  of  gyration, 
marked  under  the  diameters  in  marginal  columns-.  See  preceding  descrip- 
tion. 


LENGTH  IN  FEET. 

CONDITION 

SIZE 

20 

22 

24 

26 

28 

30  j  32 

34 

36 

OP 

ENDS. 

OP 

COLUMN. 

1440 

1120 

930 

760 

Fixed  Ends.... 

0" 

1100  810 

580 

430 

Flat  Ends  

J 

640  490 
360  260 

380 
210 

270 
170 

Hinged  Ends... 
Round  Ends  

I"  thick. 
K-  •" 

8380  2770 

2290 

1910 

1660 

1430 

1210 

1060 

910 

Fixed  Ends... 

0" 

2820  2360 

2010 

1670 

1370 

1090 

880 

710 

560 

Flat  Ends 

o 

16901  1320 

1090 

900 

750 

630 

550 

450 

370 

Ringed  Ends.  .. 

tV'  thick 

950  760 

630 

510 

420 

360 

290 

240 

210 

Round  Ends  

R=  »•>« 

5370  4670 

4080 

3540 

3020 

2650 

2250 

1960 

1770 

FMxed  Ends.  ... 

A" 

4710  3980 

3110 

2940 

2560 

2270 

1980 

1730 

1500 

Flat  Ends  

TE 

a37o 

1950 

8850 

1530 

2160 
1240 

1800 
1000 

1470 
830 

1260 
710 

1080 
620 

930 
540 

810 
450 

linged  Ends.  .. 
iound  Ends  

i"  thick. 
R-  »•*« 

6670 

6130 

5580 

5020 

4500 

4020 

3570 

3150 

2790 

Fixed  Ends.... 

K'<i 

6230 

5650 

4970 

4340 

3800 

8350!  2970 

2660 

2370 

Flat  Ends  

O 

49(50 
3460 

4370 
2680 

3630 
2140 

2990 
1720 

2480 
1440 

2120  1820 
1210  1010 

1540 
870 

1330 
760 

linged  Ends..  . 
Round  Ends.  .  .  . 

f  "  thick. 
R=  i-fc» 

7690 

7210 

6760 

6310 

5830 

5410!  4920 

4500 

4080 

Fixed  Ends.... 

fi" 

7570 

68801  6320 

5840  5280 

4770 

4240 

3800 

3410 

Flat  Ends  

u 

6280 
4540 

5610 
3900 

5060 
3360 

4570 
2870 

3980 
2380 

3420 
2000 

2900 
2390 

2480 
1440 

2160 
1240 

Hinged  Ends... 
Round  Ends  

I"  thick. 
R  =  a-30 

9010 

8550 

8160 

7820 

7470 

7130 

6760 

6390 

6040 

Fixed  Ends... 

Q" 

9010 

8530 

8120 

7760 

7250 

6750 

6320 

5930 

5540 

Flat  End.*  

O 

8050 
&430 

7450 
5690 

69:20 
5210 

6470 
4730 

5960 
4230 

5480 
3780 

5060 
3360 

4660 
2960 

426'  > 
2590 

Hinired  Ends... 
Round  Ends.  .  .  . 

*"  thick. 

R=3'OT 

10330 

9820 

9320 

8790 

8490 

8200 

7920 

7640 

7340 

Fixed  Ends... 

10" 

10330 

98-20 

9320 

87W 

8470 

8170 

7870 

7500 

7060 

Flat  Ends  

J.U 

9500 

8010 

8!»40 
7390 

8400 
6810 

7800 
6170 

7390 
5620 

6980 
5280 

6590 
4860 

6220 
4480 

5780 
4060 

Hinged  Ends.  .. 
Round  Ends.... 

i"  thick. 

R=8-8T 

11130 

10680 

10250 

9730 

9320 

8920 

8640 

8350 

8110 

Fixed  Ends... 

1  9" 

11130!10680  10250 

9730  9320 

8920  8630 

8320 

8060  Flat  Ends  

1  ft 

10350 
9030 

9880 
8440 

9410 
7910 

8840 
7300 

8400 
6810 

7960 
6340 

7600 
5940 

7180 
5490 

6860 
5130 

Hinged  Ends... 
Round  Ends.... 

f"  thick. 

R=4-65 

160  WROUGHT  IRON  AND  STEEL. 


RIVETS  AND  PINS. 

Rivets  must  be  proportioned  with  sufficient  bearing  surface  to 
resist  crushing,  and  sufficient  sectional  area  to  resist  shearing. 
Pins  must  be  proportioned  likewise,  and  also  to  safely  resist  the 
bending  action  which  usually  exists,  owing  to  the  centres  of 
pressure  being  some  distance  from  the  centres  of  supports. 

The  effective  bearing  area  of  a  rivet  or  pin  is  equal  to  its  di- 
ameter multiplied  by  the  thickness  of  the  surface  it  bears  on. 

The  shearing  area  is  the  area  of  the  cross  section  of  the  pin  or 
rivet  for  single  shear,  or  double  that  section  for  double  shear. 
For  pins,  the  pressure  on  the  pins  multiplied  by  the  leverage 
with  which  it  acts  on  the  pin  supports  is  the  bending  moment. 
(See  bending  moments,  page  78.) 

The  ultimate  crushing  strength  of  wrought  iron  is  taken  as 
equal  to  its  tensile  strength,  viz.,  50,000  Ibs.  per  square  inch, 
the  shearing  strength  at  -ft,-  of  same,  viz.,  40,000  Ibs.  per 
square  inch.  The  ultimate  modulus  of  rupture  is  taken  at 
50,000,  which  is  a  fair  estimate  for  cylindrical  sections,  as  the 
average  of  many  experiments  we  have  made  on  that  shape  gives 
nearly  that  amount.  The  annexed  table  gives  the  ultimate 
resistance  for  single  shear,  or  the  area  of  the  pin  multiplied  by 
40,000,  and  the  ultimate  resistance  to  crushing,  for  each  inch  in 
thickness  of  bearing  surface,  or  the  diameter  of  the  pin  multi- 
plied by  50,000. 

The  ultimate  bending  moments  in  inch  Ibs.  correspond  to  the 
given  diameter  of  pins,  and  are  derived  from  the  formula 

50,0007 

M.  =  ~ . 

radius 

which  can  be  reduced  to  this  form, 

M  =  6250  x  area  x  diameter,  all  in  inches. 

To  obtain  the  working  resistances,  these  ultimate  values  must 
be  divided  by  the  factor  of  safety  desirable  to  use. 

The  following  proportions  of  the  ultimate  strength  are  com- 
monly used  for  the  purposes  named. 


RIVETS  AND  PINS.  161 


For  K.  R.  bridges, 

For  light  highway  bridges, 

For  roof  trusses,  etc., 


of  ultimate  strength, 
of        "  " 

of        " 


Example. — A  pin  has  its  supports  located  three  inches  apart, 
and  bears  a  load  of  100,000  Ibs.  in  the  middle.  What  should 
the  diameter  of  the  pin  be  for  a  safety  factor  of  five  ? 

Bending  moment  =  100>00°  ^  x  3"  =  75,000  inch  Ibs. 

The  nearest  diameter  corresponding  to  this  and  taking  3  of 
the  tabular  moments,  is  4^  inches. 

The  bearing  value  of  this  pin  is  (£  of  table)  42,500  Ibs.  per 
inch  of  length,  consequently  the  thickness  of  the  metal  which 
forms  the  pin  bearings  should  be  -^W1,  or  not  less  than  2.3 
inches.  For  shear  the  pin  has  a  large  excess  of  strength,  which 
will  usually  be  found  the  case  if  properly  proportioned  other- 
wise. 

11 


162 


WROUGHT  IRON  AND   STEEL. 


ULTIMATE  STEENGTH  OF  RIVETS  AND  PINS  OF 
WROUGHT  IRON. 

For  the  working  strength  divide  the  tabular  figures  by  the  desired  factor  of 
safety. 


DIAMETER 
IN  INCHES 

OF  RIVET 
OR  PIN. 

AREA  IN 
SQUARE 
INCHES. 

ULTIMATE 
STRENGTH  FOR 
SINGLE  SHEAR 

IN  LBS. 

ULTIMATE 
CRUSHING 
STRENGTH  PER 

INCH  THICKNESS 

OF  BEARING 
SURFACE. 

ULTIMATE 
BENDING  MO- 
MENT IN 
INCH  LBS. 

X 

.196 

7840 

25000 

614 

.248 

9920 

28125 

873 

y» 

.307 

12280 

31250 

1199 

ii 

.371 

14840 

34375 

1595 

% 

.442 

17680 

37500 

2073 

\\ 

.518 

20720 

40625 

2632 

% 

.601 

24040 

43750 

3287 

1  inch. 

.785 

31400 

50000 

4906 

% 

.994 

39760 

56250 

6993 

* 

1.227 

49080 

62500 

9586 

% 

1.485 

59400 

68750 

12762 

% 

1.767 

70680 

75000 

1H566 

% 

2.074 

82960 

81250 

21065 

% 

2.405 

96200 

87500 

26305 

% 

2.761 

110440 

93750 

32357 

2  inches. 

3.141 

125660 

100000 

39263 

% 

3.547 

141880 

106250 

47109 

X 

3.976 

159040 

112500 

55913 

4.430 

177200 

118750 

65757 

% 

4.908 

196320 

125000 

76688 

% 

5.412 

216480 

131250 

88792 

K 

5.940 

237600 

137500 

102094 

6.492 

259680 

143750 

116825 

3  inches. 

7.068 

282720 

150000 

132426 

^ 

7.670         • 

806800 

156250 

149694 

% 

8.296 

331840 

162500 

168514 

% 

8.946 

357840 

168750 

188705 

9.621 

384840 

175000 

210459 

% 

10.321 

412840 

181250 

233835 

& 

11.045 

441800 

187500 

258909 

% 

11.793 

471720 

193750 

285613 

4  inches. 

12.566 

502640 

200000 

314150 

* 

13.364 

534560 

206250 

344540 

14.186 

567440 

2125CO 

376816 

% 

15.033 

601320 

218750 

411057 

% 

15.904 

636160 

225000 

447300 

% 

16.800 

672000 

231250 

485623 

* 

17.721 

708840 

237500 

526092 

18.665 

746600 

243750 

568700 

5  inches. 

19.635 

785400 

250000 

613600 

20.629 

825160 

256-250 

660773 

IX 

21.648 

865920 

26-2500 

710326 

% 

22.691 

907640 

268750 

762266 

IX 

23.758 

950320 

275000 

816667 

«/ 

24.850 

994000 

281250 

873627 

y 

25.967 

1038680 

287500 

933189 

6  inches. 

27.109 

28.274 

1084360 
1130960 

21)3750 
300000 

995410 
1060277 

STRESSES   IN   TEAMED   STEUCTURES.  163 


STEESSES  IN  SOME  SIMPLE  FORMS  OF  FRAMED 
STRUCTURES. 

Compression  indicated  by  the  sign  —  and  by  solid  lines. 
Tension  by  the  sign  +  and  by  dotted  lines. 

When  the  prefix  "stress"  is  used,  the  load  borne  by  the 
member  is  indicated;  otherwise  the  length  of  the  member  is 
meant. 

CRANES. 

Supported  at  the  points  A  and  B,  maximum  longitudinal 
stresses,  due  to  weight  W,  suspended  at  the  end.  These  stresses 
are  modified  by  the  position  of  the  hoisting  chain. 


FIG.1 


E/ 


D  is  the  point  where  a  line  drawn  from  C  at  right  angles  to 
A  B  will  intersect  the  latter. 

Stress  AC=+     -?  x  W        Stress  B  G  =  —   x  W 


"     AB=  +          x  TF  in  Fig.  2,  or  =  -          x  TFinFig.3. 

.0.  Jj  *a.  _D 

When  point  A  is  supported  by  inclined  back  stays  as  shown 
in  Fig.  1,  and  when  the  back  stay  is  in  the  plane  of  A  B  and  W 

Stress  A  E  =  +  ~  x  W  x  4-£ 

yl    JD  _fy     JrJ 

and  a  resulting  compression  ensues  on 

A  B  =  ~  -         x  W  x          » 


164 


WROUGHT  IBON  AND  STEEL. 


CRANES. 

CD 


FIG.4 


Stress  CD=- 


'AD 


W 


v  "      E  D  =  -  stress  D  0. 

Let  w  =  the  horizontal  reaction  at  B 
CD 


w  = 


AB 


xW 


B  E 
Stress  B  E  =  +  -=-=  x 

J2J   JJ 


A  E  =  +  --,  x  (stress  CD  -  w) 


E  and  H  are  points  where 
lines  drawn  from  D  intersect 
at  right  angles  A  C  and  A  B. 
X,  Y  and  Z  are  the  angles 
formed  by  extending  the  braces 
CD  and  B  D  as  indicated  by 
dotted  lines,  w  =  the  hori- 
zontal reaction  at  B 


AB 


Stress  A  C=  +  ^  x  W.     Stress  C  D  =  -  C  D 


A  D= 


or  = 


+  B  H  x  w 
—  stress  C  D  x 
-  stress  B  D  x 


«      BD 

Sine  T 
Sine  JT 

Sine  F 
SineZ 


BD 


STRESSES  IN  FRAMED  STRUCTURES.  165 

TRUSSED  GIRDERS. 
Weight  in  Middle. 
FIG.  6  Stress  A  C  or 

fty B  D^      .AC      W 


W 


"     DC=-W 


Weight  out  of  Centre. 


FIG.  7 


w, 


AB  x 


=  -  w 


FIG.  8 


W.  W. 

®  ©  o  Stress  A  HOT  DU  =  + 


xW 


Stress 


B  H  or  C  E--  W 


166 


WKOUGHT  IRON  AND   STEEL. 


TRUSSED  GIRDERS. 
Unequal  Loads  W  and  w. 


FIG.  9 


Stress  as  below  on  counter 
diagonals  B  E  orHC  according 
to  position  of  greatest  load. 

CH     fW-w\ 


Stress  <7tf= 


FIG.  10 


© 


Fink  Truss. 

Stress  B  For  D  H—  —  W 

E 

O  =  -2  W 


ID  stress1 


'=  -14  Wx 


Stress  ^1  jPor  HE= 


AO 


STRESSES  IN  FRAMED  STRUCTURES.  167 


ROOFS. 
w  —  load  concentrated  on  each  triangular  apex. 

Strut  Stresses. 
Stress  D  F=  -  w 


F          B         G 


Stresses  on  Ties. 


Rafter  Stresses. 


=:  +  l|w»  x  Stress  CE=-  2   w 


C  JT 


168  WROUGHT  IRON  AND   STEEL. 


ROOFS. 

w  —  load  concentrated  on  each  triangular  apex . 

Strut  Stresses. 

®^®     Fla'2     Bto-HInXL*-**™ 


(w) 

^-SS  i    \         !        i  ~     \          /     V    \~T>  -r\     n 


Stresses. 


ft  K-  C  B  CD\ 

-  -x-M'x  JTB; 


-_  Iw    CB  CD 

---*-W* 


Stresses  on  Ties. 
Stress  6^  /or  (7  i  =  +  -5-  x  77-^  x  7^-^ 


DB      C  B 
1BI=+    w   x 


CB 
CI=  X-~X 


^  L  =  the  sum  of  the  stresses  on  F  E  and  ^  /. 
L  B  =  the  sum  of  the  stresses  on  E  L  and  G  L. 


STRESSES  IN  FRAMED  STRUCTURES.  169 

ROOFS. 

w  =  load  concentrated  on  each  triangular  apex. 

The  rafters  and  horizontal  tie  being  each  uniformly  subdi- 
vided. 

Strut  Stresses. 

-.f  x*f 


Vertical  Ties. 
Stress  ^  if  =  +          Stress  i>  /  =  +  i/;.     Stress  G  B  = 


Rafter  Stresses. 

n    * 

Stress  C  D  =  -2   wx^± 

L  -D 
ft    A 

"     D  E  =.  —  2i  w 


Stress  at  B  =  +  2  w  x 


Horizontal  Tie. 
BA 


B  G 


B  1=  +  stress  at  B  +  I  stress  D  B  x 


+  (> 


170  WROUGHT  IRON  AND   STEEL. 

WROUGHT  IRON  SHAFTING. 

(For  steel  shafting  see  page  29.) 

The  ultimate  resistance  of  wrought  iron  to  shearing  averages 
about  -ft  of  its  ultimate  tensile  strength,  i.e.,  about  40,000 
Ibs.  per  sq.  inch  of  section.  The  torsional  resistance  of  any 
wrought-iron  shaft  can  be  determined  when  the  shearing  resist- 
ance is  known  ;  thus, 

T=  .196  d*s  for  round  shafts,  (a) 

T  =  .  28  d*s  for  square  shafts.  (b) 

d  —  diameter  of  the  shaft  in  inches. 

s  =  shearing  strength  in  Ibs.  per  sq.  inch. 

T—  the  torsional  moment  in  inch-lbs.,  that  is,  the  force  in  Ibs. 

multiplied  by  the  length  in  inches,  of  the  lever  through 

which  the  force  acts. 

Taking  s  at  40,000  Ibs.,  and  assuming  that  in  machinery  the 
working  value  of  wrought  iron  should  be  taken  at  from  one- 
fourth  to  one- fifth  of  its  ultimate  strength,  these  being  factors  of 
safety  sanctioned  by  good  practice,  we  adopt  the  mean  of  the 
two,  which  makes  the  working  resistance  to  shearing  =  9,000 
Ibs.  per  sq.  inch.  Putting  this  in  terms  of  the  torsional  moment 
and  of  the  diameter,  we  derive  from  equations  a  and  b, 

T  =  1760  d3  for  round  shafts,  (c) 

T  =  2520  d3  for  square  shafts,  (d) 


3  /     T 

—  y  .p^Q 


for  round  shafts, 


d  —  4/  ^KOA  f°r  square  shafts.  (/) 

Example  1. — What  should  be  the  diameter  of  a  round  wrought 


SHAFTING. 


171 


iron  shaft  to  safely  resist  a  force  of  1,000  Ibs.  acting  through  a 
lever  30  inches  long  ? 


-4T 


1000  x 
1700 


=  2.6  inches  diameter. 


These  formulae  apply  to  shafts  subject  to  twisting  strains 
alone.  In  practice,  however,  sucn  cases  seldom  occur,  as  shafts 
are  generally  subjected  to  combined  bending  and  twisting  strains. 
As  there  are  no  experimental  data  for  such  a  combination  of 
forces,  we  have  to  rely  on  analysis,  which  gives  the  following: 


=  M  + 


<ff) 


M  =  bending  moments  in  inch-lbs.     (See  page  78.) 

T  =±  twisting 

Tl  =  a  new  twisting  moment  which,  substituted  for  T  in  equa- 
tions (e)  and  (/),  will  give  the  desired  proportions  for 
the  shaft. 


In  revolving  shafts  the  longitudinal  stress  resulting  from  the 
bending  action  is  continually  changing  from  tension  to  com- 
pression, and  vice  versa. 

It  is  therefore  advisable,  for  reasons  given  on  page  34,  to  in- 
crease the  factor  of  safety  as  the  bending  stress  increases  com- 
paratively to  the  torsional  stress. 

The  following  changes  in  factors  of  safety  are  recommended  : 


RATIO  OP  M  TO  T. 

FACTOR  OP  SAFETY. 

DIVISOK  IN  FORMULA  (e). 

M  =  .3T  or  less, 

4 

1760 

M=  .627      " 

5 

1570 

M=T 

51 

1430 

M  =  greater  than  T, 

6 

1310 

172  WROUGHT  IRON  AND   STEEL. 

Example  2. — What  should  be  the  diameter  of  the  journals  of 
a  wrought-iron  shaft  of  a  steam  engine.  The  piston  being  12 
inches  diam.,  crank  12  inches  long,  and  the  leverage  from  centre 
of  crank  to  journal  in  the  direction  of  the  shaft  being  6  inches, 
steam  pressure  80  Ibs.  per  sq.  inch,  making  pressure  on  crank 
=  9050  Ibs.? 

T  =  9050  x  12  =  108600  inch-lbs. 
M  =  9050  x    6  =    54300        " 


(g)      771  =  54300  +  1/54300a  +  1086U02  =  175720  inch-lbs. 

Substituting  the  above  in  equation  (e),  with  the  factor  of  safety 
as  explained  above, 


d  =  4/175720  =  4.82  inches  diameter. 
V     1570 

The  following  illustrates  a  case  where  the  bending  moment  is 
greater  than  the  twisting  moment : 

Example  3. — A  non-continuous  shaft  is  so  located  that  it  must 
have  its  bearings  84  inches  apart,  and  carry  in  the  middle  a  60- 
inch  pulley  driven  by  a  12-inch  belt,  the  effective  weight  at 
centre  of  shaft  =  600  Ibs.,  and  the  belt  exercises  a  vertical  pull 
of  1000  Ibs.  What  is  the  proper  diameter  of  the  shaft  ? 

Jf=(1000+600)x84  =  33600  inch.lbs  (g 
T  =  1000  x  30  =  30000  inch-lbs. 


(g)    T1=  33600  +  t/336002  +  80000'  =  78640  inch-lbs. 

As  M  is  greater  than  T,  use  a  factor  of  safety  of  6,  which 
becomes  by  equation  (e), 

d  =  1/^2-  =  4.12  inches  diam. 

'         IdlO 

If  above  shaft  was  continuous  and  uniformly  loaded,  the 


SHAFTING.  173 

bending  moment  would  be  less.    (See  Table  of  Bending  Mo- 
ments, page  80.) 

HORSE  POWER. 

If  it  is  desired  to  find  the  relations  between  horse  power  and 
diameters  of  shafts,  the  elements  of  time  and  velocity  have  to  be 
considered.  Taking  the  horse  power  HP  at  396000  inch-lbs. 

6.28  x  T  x  V      ,        Tr 
per  minute,  we  have  HP  =  -  Q(lfirtnn  -  ,  where  V  =  revolu- 

tions  per  minute. 
rtA 

h  1      — 


y  , 

or  in  terms  of  the  diameter  by  equation  (c)  we  get, 


The  above  will  give  the  proper  diameter  of  a  shaft  for  trans- 
mitting any  desired  HP  when  the  shaft  is  subjected  to  twisting 
stress  alone,  but,  as  previously  stated,  such  a  case  seldom  occurs, 
we  must  combine  the  bending  and  twisting  stresses,  for  which  a 
general  rule  will  be  given  at  the  close  of  the  subject. 

DEFLECTION  OF  SHAFTING. 

For  continuous  line  shafting  used  for  transmitting  power  in 
shops,  factories,  etc.,  it  is  considered  good  practice  to  limit  the 
deflection  to  a  maximum  of  y^  of  an  inch  per  foot  of  length. 
The  weight  of  bare  shafting  in  Ibs.  =  2.Qd-l=  W,  or  when  as 
fully  loaded  with  pulleys  as  is  customary  in  practice,  and  allow- 
ing 40  Ibs.  per  inch  of  width  for  the  vertical  pull  of  the  belts, 
experience  shows  the  load  in  Ibs.  to  be  about  13d~l  =  W. 
Taking  the  modulus  of  transverse  elasticity  at  26,000,000  Ibs.,  we 
can  derive  from  the  authoritative  formulae  the  following  : 

I  =  \/STM2  for  bare  shafts,  (j) 

1=  ^/T75d~2  for  shafts  carrying  pulleys,  etc.,       (k) 


174  WROUGHT  IRON  AND  STEEL. 

which  would  be  the  maximum  distance  in  feet  between  bearings 
for  continuous  shafting  subjected  to  bending  stress  alone. 

If  the  length  is  fixed,  and  we  desire  the  diameter  of  the  shaft, 
we  have, 


d  —  4/  —  -  for  bare  shafting,  (?) 

*    o7o 


d  =  jy  £—  for  shafting  carrying  pulleys,  etc.        (m) 

To  apply  the  above  to  revolving  shafting  subjected  to  both 
twisting  and  bending  stress,  it  is  necessary  to  combine  equations 
(f)  and  (k)  with  equation  (»"). 

But  in  shafting,  with  the  same  transmission  of  power,  the 
torsional  stress  is  inversely  proportional  to  the  velocity  of  rota- 
tion, while  the  bending  stress  will  not  be  reduced  in  the  same 
ratio.  It  is,  therefore,  impossible  to  write  a  formula  covering 
the  whole  problem  and  sufficiently  simple  for  practical  applica- 
tion, but  the  following  rules  are  correct  within  the  range  of 
velocities  usual  in  practice. 


WORKING  FORMULA  FOR  CONTINUOUS  SHAFTING. 

For  the  diameter  (d)  in  inches,  and  the  maximum  length  (I)  in 
feet  between  bearings  of  wrought-iron  shafting  so  proportioned 
as  to  deflect  not  more  than  -rloff  of  an  inch  per  foot  of  length, 
allowance  being  made  for  the  weakening  effect  of  key  seats, 


/Kf)    I/O 

d  =  4/  ^F-  for  bare  shafts,  (») 


3  />yf\  fj"p 

d  =  y  —   —  for  shafts  carrying  pulleys,  etc.,         (o) 


I  =  ^720¥2  for  bare  shafts,  (p) 

I  =  \/l4Qd'2  for  shafts  carrying  pulleys,  etc.,  -  (q) 


SHAFTING. 


175 


In  the  event  of  the  whole  power  being  received  on  a  principal 
shaft,  the  proper  size  of  the  shaft  can  be  estimated  direct  by 
formula  (g). 

Example  4.— A  principal  shaft  receiving  150  HP  from  the 
engine,  revolves  150  R.  P.  M.,  and  is  continuous  over  bearings 
located  6  feet  apart,  the  centre  of  main  pulley  being  24  inches 
from  one  bearing  and  48  inches  from  the  other.  The  effective 
loa  1  at  the  centre  of  the  pulley  resulting  from  weight  of  pulley 
and  shaft,  and  tension  of  belt,  is  1500  Ibs.  What  should  be  the 
diameter  of  the  shaft  ? 

Note.— Excepting  special  cases  which  rarely  occur  in  practice, 
it  is  best  to  treat  such  shafts  as  non-continuous. 

By  rule  5,  page  79,  we  have, 
Jf=  WOOx:S4x_48 

tit 

and  by  formula  (7t)  we  have, 


150 
then,  by  formula  (g)  we  have 


T>=  24000  +   ^240002  +  63000"  =  92290  inch-lbs. 
and  by  formula  («), 


BELTING. 

When  designing  shafting,  allow  for  the  tension  of  belting, 
50  Ibs.  per  inch  of  width  for  single  leather  belt  or  its  equivalent, 
or  80  Ibs.  per  inch  of  width  for  double  leather  belt,  or  its  equi- 
valent of  other  material. 


176 


WROUGHT   IRON    AND    STEEL. 


WORKING  PROPORTIONS  FOR  CONTINUOUS 
SHAFTING. 


TRANSMITTING  POWER,  BUT  SUBJECT  TO  NO  BENDING  ACTION 
EXCEPT   ITS  OWN  WEIGHT. 


DIAMETER 
or  SHAFT  IN 
INCHES. 

MAX.  SAFE  TOR- 
SIONAL  MOMENT 
IN  INCH-POUNDS. 

REVOLU' 
100 

[•IONS  PER  MINUTE. 

150   |   200 

MAX.  DIS- 
TANCE IN 
FEET 

BETWEEN 

BEARINGS. 

HP 

HP 

HP 

H 

5940 

6 

10 

14 

11.7 

If 

7552 

9 

13 

17 

12.4 

n 

9433 

11 

16 

21 

13.0 

tt 

11602 

13 

20 

26 

13.6 

2 

14080 

16 

24 

32 

14.2 

2i 

16892 

19 

29 

38 

14.8 

at 

20048 

23 

34 

46 

15.4 

2| 

23580 

27 

40 

54 

16.0 

3i 

27500 

31 

47 

63 

16.5 

2* 

36603 

42 

62 

83 

17.6 

3 

47520 

54 

81 

108 

18.6 

3i 

60417 

69 

103 

137 

19.7 

&i 

75460 

86 

129 

172 

20.7 

81 

92812 

105 

158 

211 

21.6 

4 

112640 

128 

192 

256 

22.6 

SHAFTING. 


177 


WORKING  PROPORTIONS  FOR  CONTINUOUS 
SHAFTING. 


TRANSMITTING  POWER,  AND   SUBJECT  TO  BENDING  ACTION  OP 
PULLEYS,   BELTING,    ETC. 


DIAMETER 
OF  SHAFT  IN 
INCHES. 

MAX.  SAFE  TOR- 
SIOVAL  MOMENT 
IN  INCH-POUNDS. 

REVOLUI 
100 

'IONS  PER  " 
150 

MINUTE. 
200 

MAX.  DIS- 
TANCE IN 
FEET 

BETWEEN 

BEARINGS. 

HP 

IIP 

HP 

H 

5940 

5 

7 

10 

6.8 

If 

7552 

6 

9 

12 

7.2 

if 

9432 

8 

11 

15 

7.5 

if 

11602 

9 

14 

19 

7.9 

2 

14080 

11 

17 

23 

8.2 

w 

16892 

14 

21 

27 

8.6 

SH 

20048 

16 

24 

33 

8.9 

2| 

23580 

19 

29 

38 

9.2 

2* 

27500 

22 

33 

45 

9  6 

SI 

36603 

24 

36 

48 

10.2 

3 

47520 

39 

58 

77 

10.8 

3i 

60417 

49 

74 

98 

11.4 

8* 

75460 

61 

92 

123 

12.0 

3| 

92812 

75 

113 

151 

12.5 

4 

112640 

91 

137 

183 

13.1 

12 


178      AEEAS   AND    CIRCUMFERENCES    OF  CIRCLES. 


TABLE  OF  CIRCLES. 

Circumferences  or  areas  intermediate  of  those  in  the  table,  may  be  found 
by  simple  arithmetical  proportion.  The  diameters,  etc.,  are  in  inches  ;  but 
it  is  plain  that  if  the  diameters  are  taken  as  feet,  yards,  etc.,  the  other  parts 
will  also  be  in  those  same  measures. 


DlAM. 

INS. 

ClR- 
CUMP. 

INS. 

AREA. 
SQ.  INS. 

DlAM. 

INS. 

ClR- 

CUMP. 

INS. 

AREA. 
BQ.  INS. 

DlAM. 

INS. 

ClR- 
CUMF. 

INS. 

AREA. 
SQ.  INS. 

164 

.049087 

.00019 

1  15-16 

6.P8684 

2.9483 

4  15-16 

15.5116 

19.147 

1-32 

.098175 

.0  077 

2. 

6.28319 

3.1416 

5. 

15.7080 

19.635 

3-64 

.147262 

.00173 

1-16 

6.47958 

3.3410 

1-16 

15.9043 

20.129 

1-16 

.196350 

.00807 

1-8 

6.67588 

3.5466 

1-8 

16.1007 

20.629 

332 

.291524 

.00690 

3-16 

6.87223 

3.7583 

3-16 

16.2970 

21.135 

1-8 

.3'.»2699 

.01227 

1-4 

7.06858 

3.9761 

1-4 

16.4934 

21.648 

5-32 

.4.90374 

.01917 

516 

7.26493 

4.2000 

5-16 

16.6S97 

2-2.166 

3-16 

.589149 

.02761 

3-8 

7.46128 

4.4301 

3-8 

16.8861 

22.691 

7-32 

.687223 

.03758 

7-16 

7.65763 

4.6664 

7-16 

17.C824 

23.221 

1-4 

.7V5398 

.04909 

1-2 

7.85398 

4.9087 

1-2 

17.2788 

23.758 

9-32 

.8^3573 

.06213 

9-16 

8.05033 

5.1572 

9-16 

17.4751 

24.301 

5-16 

.981748 

.07670 

5-8 

8.24U68 

5.4119 

5-S 

17.6715 

24.850 

11-82 

.07992 

.09281 

11-16 

8.44303 

5.6727 

11-16 

17.8678 

25.406 

3-8 

.17810 

.11045 

3-4 

8.68938 

5.9896 

3-4 

18.0642 

25.967 

13-32 

.27627 

.12962 

13-16 

8.83573 

6.2126 

13-16 

18.2605 

26.535 

7-16 

.37445 

.15033 

7-8 

9.032  8 

6.4918 

7-8 

18.4569 

27.109 

15-32 

.47262 

.17257 

15-:  6 

9.  22*43 

6.7771 

15-16 

18.6532 

27.688 

1,2 

.57080 

.19635 

3. 

9.42478 

7.0686 

6. 

18.8496 

28.274 

17-32 

.66897 

.2-1166 

1-^6 

9.6-2113 

7.8662 

"    '1-8 

19.2423 

29.465 

9-16 

.76715 

.24850 

1-8 

9.81748 

7.6699 

l-l 

19.  (535!) 

30.6SO 

19-32 

.86582 

.27688 

3-16 

10.0138 

7.9798 

3-8 

20.0277 

31.919 

5-8 

.96350 

.30:580 

1-4 

10.2102 

s.2958 

1-2 

20.4204 

33.183 

21^32 

2.061-67 

.33824 

5-16 

10.4065 

8.6179 

5-8 

20.8131 

34.472 

11-16 

2.15984 

.37122 

3-8 

10.6029 

8.941)2 

3-4 

21.2058 

3->.785 

23-32 

2.25802 

.40574 

7-16 

10.7992 

9.2806 

7-8 

21.5984 

37.T22 

3-4 

2.  .35619 

.44179 

1-2 

10.9956 

9.6211 

7. 

Ol     Q(j  1  1 

38.485 

25-32 

2.45487 

.47937 

9-16 

11.1919 

9.9678 

1-8 

22:3888 

o9  871 

13-16 

2.55254 

.51849 

5-8 

11.3883 

10.321 

1-4 

22.7765 

41.282 

27-32 

2.65072 

.55914 

11-16 

11.1  5846 

10.680 

3-8 

23.1692 

42.718 

7-8 

2.74889 

.60132 

3-4 

11.7810 

11.045 

1-2 

23.5619 

44.179 

29-32 

2.84707 

.64504 

13-16 

11.9173 

11.416 

5-8 

23.9546 

45.664 

15-Ki 

2.!  '4524 

.69029 

7-8 

12.1737 

11.  793 

3-4 

24.3473 

47.173 

31-32 

3.04342 

.73708 

15-16 

1-2.3700 

12.177 

7-8 

24.7400 

48.7'()7 

1. 

3.14159 

.78540 

4. 

2.5664 

12.566 

8. 

25.1327 

50.265 

1-16 

3.33794 

.88664 

1-16 

12.7627 

12.<i62 

1-8 

25.5254 

51.849 

1-8 

3.53429 

.99402 

1-8 

2.9591 

18.3K4  : 

1-4 

25.9181 

53.456 

3-16 

3.73064 

.1075 

3-16 

3.1554 

13.772 

3-8 

26.3108 

55.088 

1-4 

3.9*699 

.2272 

1-4 

13.3518 

14.186 

1-2 

26.7035 

56.7'45 

5-16 

4.12334 

.3530 

5-16 

3.5481 

14.607 

5-8 

27.096-> 

58.426 

3-8 

4.31969 

.4849 

3-8 

3.744'> 

15.033 

3-4 

27.4889; 

60.132 

7-16 

4.51604 

.62:50 

7-16 

3.9108 

15.466 

7-8 

27.8816! 

61.862 

1-2 

4.71239 

.7671 

1-2 

4.1372 

15.904 

9. 

28.27431 

63.617 

9-16 

4.90874 

.9175 

9-11) 

4.3335 

16.349 

1-8 

28.6670: 

65.397 

5-8 

5.1H509 

2.0739 

5-8 

4.5299 

16.800 

1-4 

29.0597 

67.201 

11-16 

5.:-:Ol44 

2.2365 

11-16 

4.7262 

17.257 

3-8 

29.4524; 

69.  (129 

3-4 

5.49779 

2.4053 

34 

4.92-26 

17.721 

1-2 

29.84511 

70.882 

13-16 

5.69414 

2.5802 

13-16 

5.11K9 

18.190 

5-8 

30.  2378  l 

72.760 

.      7-8 

5.89049 

2.7612 

7-8 

5.3153 

18.665 

3-4 

30.6305 

74.662 

AREAS  AND    CIRCUMFERENCES   OF  CIRCLES.      179 
TABLE  OF  CIRCLES—  Continued. 


DlAM. 

INS. 

Cm- 

CUMF. 

INS. 

AREA. 

SQ.  INS. 

DlAM. 

INS. 

ClR- 
CUMF. 

INS. 

AREA. 
SQ.  INS. 

DlAM. 

INS. 

ClR- 

CUMF. 

INS. 

AREA. 
SQ.  INS. 

9  7-8 

31.0232 

76.589 

16  3-4 

52.6217 

220.35 

23  5-8 

74.2201 

438.36 

10. 

31  .4159 

78.540 

7-8 

53.0144 

223.65 

3-4 

74.6128    443.01 

1-8 

31.8086 

80.516 

17. 

53.4071 

226.98 

7-8 

75.0055    447.69 

1-4 

32.2013 

82.516 

1-8 

53.7998 

230.33 

21. 

75.3982   452.39 

3-8 

32.5940 

84.541 

1-4 

54.1925 

233.71 

1-8 

75.7909    457.11 

1-2 

3-2.9867 

86.590 

3-8 

54.5*52 

237.10 

1-4 

76.1836    461.86 

5-8 

33.3794 

88.664 

1-2 

54.9779 

240.53 

3-8 

76.5763    466.64 

3-4- 

S3.  7721 

90.763 

5-8 

55.3706 

243.98 

1-2 

76.9690!  471.44 

7-8 

34.1648 

92.886 

3-4 

55.7633 

247.45 

5-8 

77.3617    476.26 

11. 

34.5575 

95.033 

7-8 

56.1560 

250.95 

3-4 

'77.75441  481.11 

1-8 

34.9502 

97.205 

18. 

56.5487 

254.47 

7-8 

78.1471    485.98 

1-4 

35.3429 

99.402 

1-8 

56.9414 

258.02 

25. 

78.5398   490.87 

3-8 

35.7356 

101.62 

1-4 

57.3341 

261  .59 

1-8 

78.9325   495.79 

1-2 

36.1283 

103.87 

3-8 

57.7268 

265.18 

1-4 

79.3252    500.74 

5-8 

36  5210 

106.14 

1-2 

58.1195 

268.80 

3-8 

79.7179    505.71 

3-4 

36.9137 

108.43 

5-8 

58.5122 

272.45 

1-2 

80.1106    510.71 

7-8 

37.3064 

110.75 

3-4 

58.9049 

276.12 

5-8 

80.5033    515.72 

12. 

37  6991 

113.10 

7-8 

59.2976 

279.81 

3-4 

80.8960 

520.77 

1-8 

38.0918 

115.47 

19. 

59.6903 

283.53 

7-8 

81.2887 

525.84 

1-4 

38.4845 

117.86 

1-8 

60.0830 

287.27 

26. 

81.6814 

530.93 

3-8 

38.8772 

120.28 

1-4 

60.4757 

291.04 

1-8 

82.0741    536.05 

1-2 

39.2699 

122.72 

3-8 

60.8684 

294.83 

1-4 

82.4668    541.19- 

5-8 

39.6626 

125.19 

1-2 

61.2611 

298.65 

3-8 

82.8595 

546.35 

3-4 

40.0553 

127.68 

5-8 

61.6538 

302.49 

1-2 

aS.  2522 

551.55 

7-8 

40.4480 

130.19 

3-4 

62.0465 

3011.35 

5-8 

83.6449 

556.76 

13. 

40.8407 

132.73 

7-8 

62.4392 

310.24 

3-4 

84.0376 

562.00 

1-8 

41.2334 

135.30 

20. 

62.8319 

314.16 

7-8 

84.4303    567.27 

1-4 

41.6261    137.89 

1-8 

63.2246 

318.10 

27. 

84.8230 

572.56 

3-8 

42.0188    140.50 

1-4 

63.6173 

322.06 

1-8 

85.2157 

577.87 

1-2 

42.4115|   143.14 

3-8 

64.0100 

326.05 

1-4 

85.6084 

583.21 

5-8 

42.8042    145.80 

1-2 

64.4026 

330.  OH 

3-8 

86.0011 

588.57 

3-4 

43.1969 

148.49 

5-8 

64.7953 

334.10 

1-2 

86.3938    593.96 

7-8 

43.5896 

151.20 

3-4 

65.1880 

338.16 

5-8 

86.7865!  599.37 

14. 

43.9823 

153.94 

7-8 

65.5807 

342.25 

3-4 

87.1792;  604.81 

1-8 

44.3750 

156.70 

21. 

65.9734 

346.36 

7-8 

87.5719    610.27 

1-4 

44.1677 

159.48 

1-8 

66.3661 

350.50 

28. 

87.9646    615.75 

3-8 

45.1604 

162.30 

1-4 

66.7588 

354.66 

1-8 

88.35731  6  1.26 

1-2 

45.5531 

165.13 

3-8 

67.1515 

358.84 

1-4 

88.7500 

626.80 

5-8 

4*5.9458 

167.99 

1-2 

67.5442 

3(53.05 

3-8 

89.1427 

632.36 

3-4 

46.3385 

170.87 

5-8 

67.9369 

367.28 

1-2 

89.5354    637.94 

7-8 

46.7312 

173.78 

3-4 

68.3296 

371.54 

5-8 

89.9281    643.55 

15. 

47.1239 

176.71 

7-8 

68.7223 

375.  A3 

3-4 

90.3208'  649.18 

1-8 

47.5166 

179.67 

22. 

69.1150!  380.13 

7-8 

90.7135j  654.84 

1-4 

47.9093 

182.65 

1-8 

69.5077 

384.46 

29. 

91.10621  660.52 

3-8 

48.3020 

185.66 

1-4 

69.9004 

388.82 

1-8 

91.4989    666.23 

1-2 

48.6947 

188.69 

3-8 

70.2931 

393.20 

1-4 

91.8916'  671.96 

5-8 

49.0874 

191.75 

1-2 

70.6858 

397.61 

3-8 

92.2843    677.71 

3-4 

49.4801 

194.83 

5-8 

71.0785 

402.04 

1-2 

92.6770    683.49 

7-8 

49.8728 

197.93 

3-4 

71.4712 

406.49 

5-8 

93.0697    689.30 

16. 

50.2655 

201.06 

7-8 

71.8889 

410.97 

34 

93.4624 

695.13 

1-8 

50.6582 

204.22 

23. 

72.2566 

415.48 

7-8 

93.8551 

700.98 

1-4 

51.0509 

207.39 

1-8 

72.6493 

420.00 

30. 

94.2478    706.86 

3-8 

51.4436 

210.60 

1-4 

73.0420 

424.56 

18 

94.6405    712.76 

1-2 

51.8363 

213.82 

3-8 

73.4347 

429.13 

1-4 

95.0332 

718.69 

5-8 

52.2290 

217.08 

1-2 

73.8274 

433.74 

3-8 

95.4259 

724.64 

180     AREAS   AND    CIRCUMFERENCES   OF    CIRCLES. 
TABLE  OF  CIRCLES— Continued. 


DlAM. 

INS. 

CIR- 

CUMF. 

INS. 

AREA. 
SQ.  INS. 

DlAM. 

INS. 

ClR- 
CUMF. 

INS. 

AREA. 
SQ.  INS. 

DlAM. 

INS. 

CIR- 

CTJMF. 

INS. 

ARE*. 
SQ.  INS. 

30  1-2 

95.8186 

730.62 

37  3-8 

117.417 

1097.1 

44  1-4 

139.015 

1537.9 

5-8 

96.21131  736.62 

1-2 

117.810 

1104.5 

3-8 

139.408 

1546.6 

3-4 

96.6040    742.64 

5-8 

118.202 

1111.8 

1-2 

139.801 

1555.3 

7-8 

96.9967    748.69 

3-4 

118.596 

1119.2 

5-8 

140.194 

1564.0 

31. 

97.3894!  754  .-77 

7-8 

118.988 

1126.7 

3-4 

140.586 

1572.8 

18 

97.7821    760.87 

38. 

119.381 

1134.1 

7-8 

140.979 

1581.6 

1-4 

98.1748    766.99 

1-8 

119.773 

1141.6 

45. 

141.372 

1590.4 

3-8 

98.5675 

773.14 

1-4 

120.166 

1149.1 

1-8 

141.764 

1599.3 

1-2 

98.9602 

779.31 

3-8 

120.559 

1156.6 

1-4 

142.157 

1608.2 

5-8 

99.3529 

785.51 

1-2 

1*0.951 

1164.2 

3-8 

142.550 

1617.0 

3-4 

99.7456 

791.73 

5-8 

121.344 

1171.7 

1-2 

142.942 

1626.0 

7-8 

100.138 

797.98 

3-4 

121.737 

1179.3 

5-8 

143.335 

1634.9 

32. 

100.531 

804.25 

7-8 

122.129 

1186.9 

3-4 

143.728 

1643.9 

1-8 

100.924 

810.54 

39. 

122.522 

1194.6 

7-8 

144.121 

1652.9 

1-4 

101.316 

816.86 

1-8 

122.915 

1202.3 

46. 

144.513 

1661.9 

3-8 

101.709 

823.21 

1-4 

123.308 

1210.0 

1-8 

144.906 

1670.9 

1-2 

102.102 

829.58 

3-8 

123.700 

1217.7 

1-4 

145.299 

1680.0 

5-8 

102.494 

835.97 

1-2 

124.093 

1225.4 

3-8 

145.691 

1689.1 

3-4 

102.887 

842.39 

5-8 

124.486 

1233.2 

1-2 

146.084 

1698.2 

7-8 

103.280 

848.83 

3-4 

124.878 

1241.0 

5-8 

146.477 

1707.4 

33. 

103.673 

855.30 

7-8 

125.271 

1248.8 

3-4 

146.869 

1716.5 

1-8 

104.065 

861.79 

46. 

125.664 

1256.6 

7-8 

147.262 

17'25.7 

1-4 

104.458 

868.31 

1-8 

126.056 

1264.5 

47. 

147.655 

1734.9 

3-8 

104.851 

874.85 

1-4 

126.449 

1272  .4 

1-8 

148.048 

1744.2 

1-2 

105.243 

881.41 

3-8 

126.842 

1280.3 

1-4 

148.440 

1753.5 

5-8 

105.636 

888.00 

1-2 

127.2% 

1288.2 

3-8 

148.8^3 

1762.7 

3-4 

106.029 

894.62 

5-8 

127.627 

1296.2 

1-2 

149.226 

1772.1 

7-8 

106.421 

901  .26 

f-4 

128.020 

1S04.2 

5-8 

149.618 

1781.4 

34. 

106.814 

907.92 

7-8 

128.413 

1312.2 

3-4 

150.011 

1790.8 

1-8 

107.207 

914.61 

41. 

128.805 

1320.3 

7-8 

150.404 

1800.1 

1-4 

107.600 

921.32 

1-8 

129.198 

1328.3 

48. 

150.796 

1809.6 

3-8 

107.992 

928.06 

1-4 

129.591 

1336.4 

1-8 

151.189 

1819.0 

12 

108.385 

934.82 

3-8 

129.993 

1344.5 

1-4 

151.582 

1828.5 

5-8 

108.778 

941.61 

1-2 

130.376 

1352.7 

3,8 

151.975 

1837.9 

3-4 

109.170 

948.42 

5-8 

130.769 

1360.8 

1-2 

152.367 

1847.5 

7-8 

109.563 

955.25 

34 

131.161 

1369.0 

5-8 

152.760 

1&57.0 

35. 

109.956 

962.11 

7-8 

131.554 

1377.2 

3-4 

153.153 

1866.5 

1-8 

110.348 

969.00 

4ft. 

131.947 

1385.4 

7-8 

153.545 

1876.1 

1-4 

110.741 

975.91 

1-8 

132.340 

1393.7 

49. 

153.938 

1885.7 

3-8 

111.134 

982.84 

1-4 

132.732 

1402.0 

1-8 

154.881    1895.4 

1-2 

111.527 

989.80 

3-8 

133.125 

1410.3 

1-4 

154.723 

1905.0 

5-8 

111.919 

996.78 

1-2 

133.518 

1418.6 

3-8 

155.116 

1914.7 

3-4 

112.312 

1003.8 

5-8 

133.910 

1427.0 

1-2 

155.509 

1924.4 

7-8 

112.705 

1010.8 

3-4 

134.303 

1435.4 

5-8 

155.902 

1934.2 

36. 

113.097 

1017.9 

7-8 

134.  K96 

1443.8 

3-4 

156.294 

1943.9 

1-8 

113.490 

1025.0 

43. 

135.088 

1452.2 

7-8 

156.687 

1953.7 

1-4 

113.883 

1032.1 

1-8 

135.481 

1460.7 

50. 

157.080 

1963.5 

3-8 

114.275 

1039.2 

1-4 

135.874 

1469.1 

1-8 

157.472    1W3.3 

1-2 

114.668 

1046.3 

3-8 

136.267 

1477.6 

,  1-4 

157.865 

1983.2 

5-8 

115.061 

1053.5 

1-2 

136.659 

1486.2 

3-8 

158.258 

1993.1 

3-4 

115.454 

1060.7 

5-8 

137.052 

1494.7 

1-2 

158.650 

2003.0 

7-8 

115.846 

1068.0 

3-4 

137.445 

1503.3 

5-8 

159.043 

2012.9 

37. 

116.239 

1075.2 

7-8 

137.837 

1511.9 

3-4 

159.436 

2022.8 

1-8 

116.632 

1082.5 

44. 

138.230 

1520.5 

7-8 

159.829 

2032.8 

1-4 

117.024 

1089.8 

1-8 

138.623 

1529.2 

51. 

160.221 

2042.8 

ABEAS  AND   CIRCUMFERENCES   OF  CIRCLES.      181 
TABLE  OF  CIRCLES—  Continued. 


DlAM. 

INS. 

ClR- 

CUMP. 

INS. 

ARKA. 
SQ.  INS. 

DlAM. 

INS. 

CIR- 

CUMF. 

INS. 

AREA. 
SQ.  INS. 

DlAM. 

INS. 

ClR- 
CUMF. 

INS. 

AREA. 
SQ.  INS. 

51  1-8 

160.614 

2052.8 

58. 

182.212 

2642.1 

64  7-8 

203.811 

3305.6 

1-4 

161.007 

2062.9 

1-8 

182.605 

2653.5 

65. 

204.204 

3318.3 

3-8 

161.399 

2073.0 

1-4 

182.998 

2664.9 

1-8 

204.596 

3331.1 

1-2 

161.792 

2083.1 

3-8 

183.390 

2676.4 

1-4 

204.989 

3343.9 

5-8 

162.18-. 

2093.2 

1-2 

183.783 

2687.8 

3-8 

205.382 

3356.7 

3-4 

162.577 

2103.3 

5-8 

184.176 

2699.3 

1-2 

205.774 

3369.6 

7-8 

162.970 

2113.5 

3-4 

184.569 

2710.9 

5-8 

206.167 

3382.4 

52. 

163.363 

2123.7 

7-8 

184.961 

2722.4 

3-4 

206.560 

3395.3 

1-8 

163.756 

2133.9 

59. 

185.354 

2734.0 

7-8 

2-  6.952 

3408.2 

1-4 

164.  14S 

2144.2 

1-8 

185.747 

2745.6 

66. 

207.345 

3421.2 

3-8 

164.541 

2154.5 

1-4 

186.139 

2757.2 

1-8 

207.738 

3434.2 

1-2 

164.934 

2164.8 

3-8 

186.532 

2768.8 

1-4 

208.131 

3447.2 

5-8 

165.336 

2175.1 

1-2 

186.925 

2780.5 

3-8 

208.523 

3460.2 

3-4 

165.719 

2!85.4 

5-8 

187.31? 

2792.2 

1-2 

208.916 

3473.2 

7-8 

166.112 

2195.8 

3-4 

187.7KI 

2803.9 

5-8 

209.309 

3486.3 

53. 

166.504 

2203.2 

7-8 

188.103 

2815.7 

3-4 

209.701 

3499.4 

1-8 

166.897 

2216.6 

60. 

188.496 

2827.4 

7-8 

210.  ('94 

a512.5 

1-4 

167.290 

2227.0 

1-8 

188.888 

2839.2 

67. 

210.487 

3525.7 

3-8 

167.683 

2237.5 

1-4 

189.281 

2851.0 

1-8 

210.879 

b538.8 

1-2 

168.075 

2248.0 

3-8 

189  674 

2862.9 

1-4 

211.272 

3552.0 

5-8 

168.468 

2253.5 

1-2 

190.066 

2874.8 

3-8 

211.665 

a565.2 

3-4 

168.861 

22(39.1 

5-8 

191.459 

2S86.6 

1-2 

212.058 

3578.5 

7-8 

169.253 

2279.6 

3-4 

190.852 

2898.6 

5-8 

212.450 

3.391.7 

54. 

169.646 

2290  2 

7-8 

191.244 

2910.5 

3-4 

212.843 

3605.0 

1-8 

170.039 

2300.8 

61. 

191.6*7 

2922.5 

7-8 

213.236 

3618.3 

1-4 

170.431 

2311.5 

1-8 

192.030 

2934.5 

68. 

213.628 

3631.7 

3-8 

170.824 

2322.1 

1-4 

192.423 

2916.5 

1-8 

214.021 

3645.0 

1-2 

171.217 

2332.8 

3-8 

192.815 

2958.5 

1-4 

214.414 

3658.4 

5-8 

171.609 

2343.5 

1-2 

193.  20s 

2970.6 

3-8 

214.806 

3671.8 

3-4 

172.002 

2354.3 

5-8 

193.601 

2982.7 

1-2 

215.199 

3685.3 

7-8 

172.  &95 

2365.0 

3-4 

193.993 

5994.  8 

5-8 

215.592 

3698.7 

55. 

172.788 

2375.8 

7-8 

194.388 

3006  9 

3-4 

215.984 

3712.2 

1-8 

173.180 

2386.6 

62. 

194.779 

3(119.1 

7-8 

216.377 

3725.7 

1-4 

173.573 

2397.5 

1-8 

195.171 

3031.3 

69. 

216.770 

3789.3 

3-8 

173.966 

2108.3 

1-4 

195.564 

3043.5 

1-8 

217.  163 

3752.8 

1-2 

174.358 

2419.2 

3-8 

195.957 

3055.7 

1-4 

217.555 

3766.4 

5-8 

174.751 

24:30.1 

1-2 

196.350 

3068.0 

38 

217.948 

3780.0 

3-4 

175.144 

2441  .1 

5-8 

196.742 

3080.3 

1-2 

218.341 

3793.7 

7-8 

175.536 

2452.0 

3-4 

197.135 

3092.6 

5-8 

218.733 

3807.3 

56. 

175.929 

2463.0 

7-8 

197.528 

3104.9 

3-4 

219.126 

3821.0 

1-8 

176.3-22 

2474.0 

63. 

197.920 

3117.2 

7-8 

219.519 

3834.7 

1-4 

176.715 

2485.0 

1-8 

198.313 

3129.6 

70. 

219.911 

3H48.5 

3-8 

177.107 

2496.1 

1-4 

198.706 

3142.0 

1-8 

220.304 

3862.2 

1-2 

177.500 

2507.2 

3-8 

199.098 

3154.5 

1-4 

220.697 

3876.0 

5-8 

177.893 

2518.3 

1-2 

199.491 

3166.9 

3-8 

221.000 

3889.8 

3-4 

178.285 

2529.4 

5-8 

199.884 

3179.4 

1-2 

221.482 

3903.6 

7-8 

178.678 

2540.6 

3-4 

200.277 

3191.9 

5-8 

221.875 

3917.5 

57. 

179.071 

2551.8 

7-8 

200.669 

3204.4 

3-4 

222.268 

3931.4 

1-8 

179.463 

2563.0 

61. 

201.062 

3-217.0 

7-8 

222.660 

3945.3 

1-4 

179.856 

2574.2 

1-8 

201.455 

3229.6 

71. 

223.053 

3959.2 

3-8 

180.249 

2585.4 

1-4 

201.847 

3242.2 

1-8 

223.446 

3973.1 

1-2 

180.642 

2596.7 

3-8 

202.240 

3254.8 

1-4 

223.838 

3987.1 

5-8 

181  .034 

2608.0 

1-2 

202.633 

3267.5 

3-8 

224.231 

4001.1 

3-4 

181.427 

2619.4 

5-8 

203.025 

3280.1 

1-2 

224.624 

4015.2 

7-8 

181.820 

2630.7 

3-4 

203.418 

3292.8 

5-8 

225.017 

4029.2 

182      AREAS  AND   CIRCUMFERENCES    OF  CIRCLES. 
TABLE  OF  CIRCLES— Continued. 


DlAM. 

INS. 

ClB- 

CUMP. 

INS. 

AREA. 
SQ.  INS. 

DlAM. 

INS. 

ClR- 
CUMP. 

INS. 

AREA. 
SQ.  INS. 

DlAM. 

INS. 

ClR- 

CUMF. 

INS. 

AREA. 
SQ.  INS. 

713-4 

225.409 

4043.3 

78  5-8 

247.008 

4855.2 

85  1-2 

268.606 

5741.5 

7-8 

225.802    4057.4 

3-4 

247.400 

4870.7 

5-8 

268.999 

5758.3 

72. 

226.195    4071.5 

7-8 

247.793 

4886.2 

3-4 

269.392 

5775.1 

1-8 

226.587 

4085.7 

79. 

248.186 

4901.7 

7-8 

269.784 

5791  .9 

1-4 

226.980 

4099.8 

1-8 

248.579 

4917.2 

86. 

270.177 

5808.8 

3-8 

227.373    4114.0 

1-4 

248.971 

4932.7 

1-8 

270.570 

5825.7 

1-2 

227.765 

4128.2 

3-8 

249.364 

4948.3 

1-4 

270.962 

5842.6 

5-8 

228.158 

4142.5 

1-2 

249.757 

4963.9 

3-8 

271.1355 

5859.6 

3-4 

828.551 

4156.8 

5-8 

250.149 

4979.5 

1-2 

271.748 

5876.5 

7-8 

228  9441  4171.1 

3-4 

250.542 

4995.2 

5-8 

272.140 

5893.5 

73. 

229.  a36 

4185.4 

7-8 

250.935!  5010.9 

3-4 

272.533 

5910.6 

1-8 

229.729 

4199.7 

80. 

251.  327  i  5026.5 

7-8 

272.926 

5927.6 

1-4 

230.122 

4214.1 

1-8 

25l.720|  5042.3 

87. 

273.319 

5944.7 

3-8 

230.514 

4228.5 

1-4 

252.113    5058.0 

1-8 

273.711 

5961.8 

1-2 

230.907 

4242.9 

3-8 

252.506   5073.8 

1-4 

274.104 

5978.9 

5-8 

231.300 

4257.4 

1-2 

252.898    5089.6 

3-8 

274.497    5996.0 

3-4 

231.692 

4271.8 

5-8 

253.291    5105.4 

1-2 

274.889    6013.2 

7-8 

232.085 

4286.3 

3-4 

253.684    5121.2 

5-8 

275.282    6030.4 

74. 

232.478 

4300.8 

7-8 

254.076 

5137.1 

3-4 

275.675    6047.6 

1-8 

232.871 

4315.4 

81. 

254.469 

5153.0 

7-8 

276.067 

6064.9 

1-4 

233  263 

4329.9 

1-8 

254.862 

5168.9 

88. 

276.460 

6082.1 

3-8 

233.656 

4:i44.5 

1-4 

255.254    5184.9 

1-8 

276.853!  6099.4 

1-2 

234.049 

4359.2 

3-8 

255.647    5200.8 

1-4 

277.246!  6116.7 

5-8 

234.441 

4373.8 

1-2 

256.0401  5216.8 

3-8 

277.638 

6134.1 

3-4 

234.834 

4388.5 

5-8 

256.433!  5232.8 

1-2 

278.031 

6151.4 

7-8 

235.2271  4403.1 

3-4 

256.8251  5248.9 

5-8 

278.424 

6168.8 

75. 

235.619 

4417.9 

7-8 

257.218!  5264.9 

3-4 

278.816 

6186.2 

1-8 

236.012 

4432.6 

82. 

257.6111  5281.0 

7-8 

279.209 

6203.7 

1-4 

236.405    4447.4 

1-8 

258.003 

5297.1 

89. 

279.602 

6221.1 

3-8 

236.798    4462.2 

1-4 

258.396 

5313.3 

1-8 

279.994 

6238.6 

1-2 

237.190|  4477.0 

3-8 

258.789 

5329.4 

1-4 

280.387 

6256.1 

5-8 

237.583!  4491.8 

1-2 

259.181 

5345.6 

3-8 

280.780 

6273.7 

3-4 

237.976!  4506.7 

5-8 

259.574 

5361.8 

1-2 

281.173 

6291.2 

7-8 

238.368    4521.5 

3-4 

259.967 

5378.1 

5-8 

281.565 

6308.8 

76. 

2:«.761 

4536.5 

7-8 

260.359 

5394.3 

3-4 

281.958 

6326.4 

1-8 

239.154 

4551.4 

83. 

260.752 

5410.6 

7-8 

282.351 

6344.1 

1-4 

239.546    4566.4 

1-8 

261.145 

5426.9 

90. 

282.743 

6361.7 

3-8 

239.939    4581.3 

1-4 

261.538 

5443.3 

1-8 

283.136 

6379.4 

1-2 

240.332    4596.3 

3-8 

261.930 

5459.6 

1-4 

283.529 

6397.1 

5-8 

240.725    4611.4 

1-2 

262.323 

5476.0 

3-8 

283.921 

6414.9 

3-4 

241.1171  4626.4 

5-8 

262.716 

5492.4 

1-2 

284.314 

6432.6 

7-8 

241.510!  4641.5 

3-4 

263.108 

5508.8 

5-8 

284.707 

6450.4 

77. 

241.903:  4656.6 

7-8 

263.501 

5525.3 

3-4 

285.100 

6468.2 

1-8 

242.295J  4671.8 

84. 

263.894 

5541  .8 

7-8 

285.492 

6486.0 

1-4 

242.688   4686.9 

1-8 

264.286 

5558.3 

91. 

285.885 

6503.9 

3-8 

243.081    4702.1 

1-4 

264.679 

5574.8 

1-8 

286.278 

6521.8 

1-2 

243.473   4717.3 

3-8 

265.072 

5591.4 

1-4 

286.670 

6539.7 

5-8 

243.866:  4732.5 

1-2 

265.465 

5K07.9 

3-8 

287.063 

6557.6 

3-4 

244.259!  4747.8 

5-8 

265.857 

5K24.5 

1-2 

287.456 

6575.5 

7-8 

244.652    4763.1 

3-4 

266.250 

5641.2 

5-8 

287.848 

6593.5 

78. 

245.044!  4778.4 

7-8 

266.643 

5657.8 

3-4 

288.241 

6611.5 

1-8 

245.437   4798.7 

85. 

267.035 

5674.5 

7-8 

288.  634 

6(i29.6 

1-4 

245.830    4809.0 

1-8 

267.428 

5691.2 

92. 

289.027 

6647.6 

3-8 

246.222 

4824.4 

14 

267.821 

5707.9 

1-8 

289.419 

6665.7 

1-2 

246.615 

4839.8 

3-8 

268.213 

5724.7 

1-4 

289.812 

6683.8 

AKEAS  AND   CIKCUMFERENCES  OF  CIECLES.      183 
TABLE  OF  CIRCLES— Continued. 


DlAM. 

INS. 

ClR- 
CUMF. 

INS. 

AREA. 
SQ.  INS. 

DlAM. 

INS. 

ClR- 
CUMF. 

INS. 

ABE  A. 
SQ.  INS. 

DlAM. 

INS. 

Cm- 

CUMF. 

INS. 

A"KA. 

SQ.  INS. 

92  3-8 

290.205 

6701.9 

95. 

298.451 

7088.2 

97  5-8 

306.698 

7485.8 

1-2 

290.597 

6720.1 

1-8 

298.844    7106.9 

3-4 

307.091    7504.5 

5-8 

290.990 

6738.2 

1-4 

299.237    7125.6 

7-8 

807.468    7523.7 

3-4 

291.383 

6756.4 

3-8 

299,629    7144.3 

98. 

307.876    7543.0 

7-8 

291.775 

6774.7 

1-2 

300.022    716::.  0 

1-8 

308.269    7562.2 

93. 

292.168 

6792.9 

5-8 

300.415    7181.8 

1-4 

308.661    7581.5 

1-8 

292.561 

6811.2 

3-4 

800.807    7-J00.6 

3-8 

309.054 

7600.8 

1-4 

292.954 

6829.5 

7-8 

301.  200  :   7219.4 

1-2 

309.447 

7620.1 

3-8 

293.346 

6847.8 

96. 

301.593    7238.2 

5-8 

809.840    7639.5 

1-2 

293.739 

6866.1 

1-8 

301.986 

7257.1 

3-4 

310.232    7658.9 

5-8 

294.132 

6884.5 

1-4 

302.3781  7276.0 

7-8 

310.625    7678.3 

3-4 

294.524 

6902.9 

3-8 

302.771    7294.9 

199. 

311.018    7697.7 

7-8 

294.917 

6921.3 

1-2 

303.1  64    7313.8 

1-8 

311.410    7717.1 

M. 

295.310 

6939.8 

5-8 

303.556-  7332.8 

1-4 

311.803!  7736.6 

1-8 

295.702 

6958.2 

3-4 

303.949    7351.8 

3-8 

312.1961  7756.1 

1-4 

29(5.095 

6976.7 

7-8 

304.342    7370.8 

1-2 

312.588    7775  6 

3-8 

296.488 

691)5.3 

97. 

304.734    7389.8 

5-8 

312.981J  7795.2 

1-2 

296.881 

7013.8 

1-8 

305.127    7408.9 

3-4 

313.374    7814.8 

5-8 

297.273 

7082.4 

1-4 

305.520    7428.0 

7-8 

313.767|  7834.4 

3-4 

297.666 

7051.0 

3-8 

305.913    7447.1 

100. 

314.159    7854.0 

7-8 

298.059 

7069.6 

1-2 

306.305 

7466.2 

184 


WEIGHT  OF  ROLLED  IEON. 


WEIGHT  OF  A  LINEAL  FOOT  OF  ROUND  AND  SQUAKlS 
IRON. 


SIZE  IN 
INCHES. 

BOUNDS. 

SQUARES. 

SIZE  IN 
j  INCHES. 

ROUNDS. 

SQUARES. 

WEIGHT 
PER  FOOT. 

WEIGHT 
PER  FOOT. 

WEIGHT 
PER  FOOT. 

WEIGHT 
PER  FOOT. 

& 

0.01 

0.013 

3f 

29.82 

37.969 

JL 

0.041 

0.052 

3a 

32.07 

40.833 

A 

0.092 

0.117 

*| 

34.40 

43.802 

i 

0.163 

0.208 

3* 

36.813 

46.875 

i 

0.363 

0.468 

31 

39.31 

50.052 

0.654 

0.833 

4* 

41.887 

53.333 

& 

1.023 

1.302 

4* 

44.547 

56  719 

f 

1.472 

1.875 

4} 

47.287 

GO.  208 

2.004 

2.552 

41 

50.11 

63.802 

i 

2.618 

3.333 

41 

53.013 

67.50 

H 

3.313 

4.218 

4f 

56.00 

71.302 

U 

4.09 

5.208 

59.057 

75.208 

U 

4.947 

6.302 

4 

62.217 

79.219 

H 

5.89 

7.50 

5 

65.45 

83.333 

if 

6.01 

8.802 

51 

68.763 

87.552 

11 

8.017 

10.208 

8 

72.157 

91.875 

11 

9.203 

11.718 

5f 

75.633 

96.302 

2 

10.47 

13.333 

5  1 

79.197 

100.833 

3| 

11.82 

15.052 

'5f 

82.833 

105.468 

2V 

13.253 

16.875 

86.557 

110.208 

21 

14.766 

18.803 

5| 

90.36 

115.052 

3* 

16.36 

20.833 

6 

94.247 

120.00 

81 

18.036 

22.969 

(ji 

102.263 

130.208 

19.797 

25.208 

6^ 

110.61 

140.833 

3 

23.56 

30.00 

6| 

119.28 

151.875 

3i 

25.563 

32.552 

7 

128.28 

163.333 

51 

27.65 

35.208 

WEIGHT   OF   KOLLED   IRON. 


185 


WEIGHT  OF  A  LINEAL  FOOT  OF  FLAT  IRON. 


|  Width  in  Inches.  1 

THICKNESS  IN  INCHES. 

A 

8 

* 

i 

ft 

1 

* 

* 

SL 

1 

I 

8 

1 

i 

0.16 

0.31 

0.47 

0.63 

0.77 

0.94 

1.09 

1.25 

1.56 

1.8* 

2.18 

2.50 

JO.  18 

0.360.55 

0.73 

0.91 

1.09 

1.28 

1.46 

1.83 

2.19 

2.5b 

2.92 

1    0.210.420.62 
H  0.23(0.47,0.70 

0.83 
0.94 

1.04 
1.17 

1.25 
1.41 

1.46 
1.64 

1.67 
1.68 

2.  08 
2.34 

2.50 
2.81 

2.92 

3.28 

3.33 
3.75 

HO.  26 

0.520.78 

1.04 

1.30 

1.56 

1.82 

2.08 

2.60 

3.12 

3.64 

4.17 

1£0.29 

0.57  0.86 

1.15 

1.43 

1.72 

2.00 

2.29 

2.86 

3.44 

4.01 

4.58 

HO.  31 

0.630.94 

1.25 

1.56 

1.88 

2.19 

2.50 

3.13 

3.75 

4.38 

5.00 

110.34 

0.681.02 

1.35 

1.69 

2.03 

2.37 

2.71 

3.38 

4.06 

4.74 

5.42 

HO.  36 

0.73 

1.09 

1.46 

1.82 

2.19 

2.55 

2.92 

3.65 

4.37 

5.10 

5.83 

If  0.39 

0.78 

1.17 

1.56 

1.95 

2.34 

2.73 

3.12 

3.91 

4.68 

5.46 

6.25 

2 

0.42 

0.83 

1.24 

1.67 

2.08 

2.50 

2.92 

3.33 

4.17 

5.00 

5.  as 

6.67 

2^0.44 

0.89 

1.33 

1.77 

2.21 

2.66     3.10 

3.54 

4.43 

5.31 

6.20 

7.C8 

2i0.47 

0.94 

1.41 

1.88 

2.34 

2.81 

3.28 

3.75 

4.69 

5.63 

6.56 

7.50 

2f  0.49 

0.991.48 

1.98 

2.47 

2.96 

3.46 

3.96 

4.95 

5.94 

6.93 

7.92 

2J0.52 

1.041.56 

2.08 

2.60 

3.12 

3.64 

4.17 

5.21 

6.25 

7.29 

8.33 

2|0.55 

1.091.64 

2.19 

2.73 

3.2S 

3.83 

4.38 

5.47 

6.56 

7.66 

8.75 

2f  0.57 

1.141.72 

2.29 

2.86 

3.44 

4.01 

4.59 

5.73 

6.87 

8.02 

9.17 

2J0.60 

1.201.80 

2.40 

2.99 

3.59 

4.19 

4.79 

5.99 

7.19 

8.38 

9.58 

3 

0.62 

1.251.87 

2.50 

3.12 

3.75 

4.37 

5.00 

6.25 

7.50 

8.75 

10.00 

3f0.68 

1.352.03 

2.71 

3.38 

4.07 

4.74 

5.42 

6.77 

8.12 

9.48 

10.83 

3i0.73 

1.462.19 

2.92 

3.65 

4.38 

5.11 

5.83 

7.29 

8.75 

10.21 

11.67 

3f  0.78 

1.562.34 

3.12 

3.90 

4.69 

5.47 

6.25 

7.81 

9.37 

10.94 

12.50 

4 

0.83 

1.672.50 

3.33 

4.17 

5.00 

5.83 

6.67 

8.33 

10.00 

11.67 

13.33 

4*0.94 

1.872.81 

3.75 

4.69 

5.63 

6.56 

7.50 

9.38 

11.25 

13.13 

15.00 

5 

1.04 

2.083.13 

4.17 

5.21 

6.251     7.30 

8.34 

10.42 

12.50 

14.59 

10.67 

6 

1.25 

2.503.75 

5.00 

6.25 

7.50 

8.75 

10.00 

12.50 

15.00 

17.50 

20.00 

7 

1.46 

2.924.37 

5.83 

7.29 

8.75 

10.20 

11.67 

14.58 

17.50 

20.42 

23.33 

8 

1.67 

3.335.00 

6.67 

8.34 

10.00 

11.67 

13.33 

16.67 

20.00 

23.33 

26.67 

9 

1.87 

3.755.62 

7.50 

9.37 

11.25 

13.12 

15.00 

18.75 

22.50 

26.25 

30.00 

102.08 

4.176.25 

8.33 

10.42 

12.50 

14.58 

16.67 

20.83 

25.00 

29.17 

33.33 

11 

2.29 

4.586.87 

9.17 

11.46 

13.75 

16.04 

18.33 

22.92 

27.50 

32.08 

36.67 

12J2.50 

5.007.50 

10.00 

12.50 

15.00 

17.50 

20.00 

25.00 

30.00 

35.00 

40.00 

186        DECIMAL  EQUIVALENTS  FOB  FRACTIONS. 


DECIMAL    EQUIVALENTS    FOR   FRACTIONS  OF 
AN  INCH. 


FRACTION. 

DECIMAL. 

FRACTION. 

DECIMAL. 

* 

.015625 

33. 

.515625 

.03125 

|l 

.53125 

ft 

.046875 

H 

.546875 

5s 

.0625 

ft 

.5625 

A 

.078125 

11 

.578125 

.09375 

l£ 

.59375 

ft 

.109375 

II 

.609375 

j_ 

9 

.125 

1 

.625 

J 

.140625 

AL 

.640625 

i 

.15625 
.171875 

II 

'.  671875 

.1875 

!i 

.6875 

.203125 

fl 

.703125 

.21875 

^.a. 

.71875 

.234375 

il 

.734375 

* 

.25 

4 

.75 

tt 

.265625 

h4 

.765625 

V 

.28125 

« 

.78125 

32" 

.296875 

^1 

.796875 

•5£ 

.3125 

ft 

.8125 

ti 

.328125 

f! 

.828125 

XI 

.34375 

21 

.84375 

II 

.359375 

64* 

.859375 

f 

.375 

M 

1 

.875 

2/L 

.390625 

H 

.890625 

1  | 

.40625 

ft 

.90625 

li 

.421875 

.921875 

?y 

.4375 

11 

.9375 

^a 

.453125 

H 

.953125 

Vs 

.46875 

31. 

.96875 

fi 

.484375 

It 

.984375 

.5 

STANDARD   SEPARATORS   FOR  PENCOYD   BEAMS.     187 


STANDARD  SEPARATORS  FOR  PENCOYD  I  BEAMS. 


CHART 
No. 

SIZE  OF  BEAM. 

Weieht  of 
separator. 

JS 

§-S 

5   K^ 

•s§* 
ill 
jr-s 

BOLTS,  A. 

Weight  of  each 
complete  bolt. 

jjf 

No. 

SIZE. 

1 

15  "  Heavy 

22 

3.84 

2 

r 

1.75 

.123 

2 

15  "  Light 

21 

3.13 

2 

3." 

1.62 

.123 

3 

12  "  Heavy 

16 

2.76 

2 

" 

1.69 

.123 

4 

12  "  Light 

14? 

2.95 

2 

li" 
4 

1.58 

.123 

5 

10£"  Heavy 

in 

2.10 

1 

3." 
4 

1.64 

.123 

51 

lO.f"  Medium 

11 

2.06 

1 

2" 
4 

1.28 

.123 

6 

10|"  Light 

11 

2.03 

1 

1" 

1.53 

.123 

7 

10  "  Heavy 

10 

1.93 

1 

" 

4 

1.56 

.123 

8 

10  "  Light 

10 

1.93 

1 

r 

1.52 

.123 

9 

<J  "  Heavy 

QL 

1.63 

1 

t" 

1.52 

.123 

10 

9  "  Light 

9 

1.63 

1 

r 

1.48 

.123 

11 

8  "  Heavy 

6| 

1.36 

1 

1.50 

.123 

12 

8  "  Light 

6i 

1.49 

1 

4 

1.46 

.123 

13 

7  "  Heavy 

4 

1.26 

1 

fi." 

0.96 

.085 

14 

7  "  Light 

4 

1.26 

1 

1" 

0.91 

.085 

15 

6  "  Heavy 

3 

1.24 

1 

8"" 

0.90 

.085 

16 

6  "  Light 

3 

1.24 

1 

t;| 

0.87 

.085 

17 

5  "  Heavy 

2f 

1.10 

1 

0.43 

.055 

18 

5  "  Light 

2J 

1.10 

1 

i" 

0.42 

.055 

19 

4  "  Heavy 

2 

0.85 

1 

i" 

0.42 

.055 

20 

4  "  Light 

2 

0.85 

1 

i" 

0.39 

.055 

21 

3  "  Heavy 

1^. 

0.69 

1 

i" 

0.38 

.055 

22 

3  "  Light 

il 

0.69 

1 

r 

0.31 

.055 

The  figures  in  the  third  column  are  the  weights  in  Ibs.  for  cast  iron  sepa- 
rators suitable  for  beams,  placed  with  flanges  in  contact.  When  the  flanges 
are  separated,  add  the  amount  corresponding  to  the  distance  of  separation, 
given  in  the  fourth  column.  In  the  same  way  the  weight  of  bolts  may  be 
obtained  in  the  final  columns. 

Example.— A  pair  of  12"  heavy  beams  have  the  flanges  separated  H  inches, 
the  weight  of  one  separator  will  be  2.76  x  H  +  1(5  =  20.14  Ibs.  One  f  bolt 
complete  and  suitable  for  close  flanges,  will  weigh  1.G9  Ibs.  Add  to  this  .123 
x  1±  =  1.88,  which  is  the  weight  of  bolt  required. 


188 


BOLTS  AND  NUTS. 


BOLTS  AND  NUTS. 
MANUFACTURER'S  STANDARD. 


WEIGHT 

OP  HEAD 

WEIGHT 

Si 

ZE  OP  Nu 

T» 

DlAMETEK 

AND 

NUT. 

OP  BOLT 

Of 

BODIES 

PER  INCH 

Width. 

Thick- 
ness. 

Hole. 

BOLT. 

Square. 

Hexagon. 

OF 

LENGTH. 

I 

A 

1 

A 

.034 
.067 

.031 
.055 

.014 
.021 

1 

A 

.110 
.181 

.105 
.171 

.031 
.042 

1 

t 

f 

.210 

.192 

.055 

1 

^ 

r. 

1 

.280 

.233 

.055 

H 

•j^. 

i 

.369 

.335 

.069 

4 

1 

* 

b. 

.431 

.403 

.085 

u 

5. 

5. 

.545 

.475 

.085 

if 

a. 

563 

.085 

*f 

I 

.776 

.673 

.123 

l£ 

i 

.770 

.123 

ll 

i 

.964 

.123 

if 

1 

1.34 

1.14 

.167 

l| 

1 

3-5- 

i 

1.19 

.167 

1 

fft 

i 

1.28 

.167 

j| 

37 

1 

1.46 

.167 

l| 

i 

? 

1.75 

1.48 

.218 

13- 

u 

1 

1.65 

.218 

2* 

l8 

1 

1 

2.24 

.218 

2 
2 

l| 

ft 

| 

2.47 

2:48* 

.276 
.276 

o  i 

1— 

44 

1    1 

3  14 

276 

2i 

ll 

ID 

jl 

3.'74 

.341 

4 

if 

1-jlg. 

l| 

3'.46 

.341 

01 

1"4 

ITF 

H 

4.47 



.341 

2| 

H 

IfV 

li 

4.63 

.412 

2J 

If 

1'fV 

l| 

5.85 



.412 

2| 

H 

1'rff 

H 

6.11 

.491 

3 

IA 

7.59 



.491 

BOLTS  AND   NUTS. 


189 


BOLTS  AND  NUTS. 
MANUFACTURER'S  STANDARD. 


WEIGHT  OF  HEAD 

WEIGHT 

SIZE  OF  NUT. 

DIAMETER 

AND  NUT. 

OF  BOLT 

BODIES 

OP 

PER  INCH 

Width. 

Thick- 

liCSS. 

Hole. 

BOLT. 

Square. 

Hexagon. 

OF 

LENGTH. 

3 

1} 

liV 

If 

7.65 

.570 

If 

1'Hf 

If 

(K48 

.... 

.576 

&* 

H 

1  -i^ 

lj 

9.42 

.668 

3? 

If 

1-1% 

If 

li.'9 

.668 

3? 

2 

1H 

H 

.... 

li.'e' 

.767 

P 

If 

2 

1 

If 

2 

14.1 

12^6 

.767 
.872 

3* 

2» 

Mi 

2 

.... 

12.6 

.872 

4 

2 

Ht 

2 

18.6 

.... 

.872 

4 

2*L 

H 

2$ 

18.9 

.... 

.985 

4 

*i 

2 

5J 

19.3 

.... 

1.104 

The  preceding  tables  for  bolts  and  nuts  include  the  sizes  of 
nuts  usually  applied  to  structural  work. 

The  sizes  known  as  "  U.  S."  or  "  Franklin  Inst."  standard, 
used  on  finished  machines,  are  lighter  than  the  foregoing. 

The  weights  given  in  the  fifth  and  sixth  columns  are  for  a 
head  and  nut,  or  for  two  nuts,  including  the  portion  of  the  bolt 
body  contained  in  the  nuts. 

The  final  column  is  the  weight  of  bolt  bodies  of  round  iron  per 
inch  of  length.  To  obtain  the  weight  of  any  bolt  :  multiply  the 
amount  in  final  column  by  the  clear  length  between  nuts  in 
inches  and  add  in  the  weight  of  nuts  as  given  in  the  fifth  or  sixth 
column. 

Example. — What  is  the  weight  of  a  bolt  f"  diam.  .and  20" 
long  between  nuts,  the  nuts  being  If"  sq.  x  |"  ?  .123  x  20  = 
2.46  +  .77  =  3.23lbs. 


190        WEIGHT   OF  BRIDGE   RIVETS  IN  POUNDS. 


WEIGHT  OF  BRIDGE  RIVETS  IN  POUNDS 


DIAMETER  or  KIVET. 

WEIGHT  OP  Two  HEADS. 

WEIGHT  OF  BODY  PER 
INCH  OF  LENGTH. 

t 

.036 

.031 

A 

.058 

.OJ2 

J 

.080 

.054 

& 

.120 

.069 

1 

.160 

.085 

& 

.210 

.103 

t 

.260 

.123 

it 

.350 

.144 

1 

.440 

.167 

H 

.540 

.192 

i 

.640 

.218 

ttir 

.714 

.246 

11 

.788 

276 

i* 

1.07 

.341 

This  table  applies  to  rivets  whose  heads  are  a  spherical  seg- 
ment, the  contents  being  equal  to  a  hemisphere  whose  diameter 
equals  1|  diameters  of  the  rivet  shank  plus  -f^th  of  an  inch. 
To  find  the  weight  of  rivets,  take  the  total  thickness  of  material 
to  be  riveted,  which  will  be  the  length  of  the  rivet  between 
heads,  and  multiply  this  by  the  weight  per  inch  of  length  of 
rivet  shank,  and  add  in  the  weight  of  the  two  heads. 

Example.— Three  f  inch  plates  are  to  be  riveted  together  with 
|  inch  rivets,  required  the  weight  of  each  rivet.  The  length  of 
rivet  shank  equals  3  x  f  =  2k  inches.  Then  2i  x  .167=  .376, 
to  which  add  the  weight  of  the  heads  .44,  making  .816  Ib.  for 
each  rivet. 


INDEX. 


Angle  bars,  explanation  of  tables  of  dimensions 1 

"        "      weights  per  yard  of  various  thicknesses 8,  9 

Angles,  sq.  root,  weights  per  yard  of  various  thicknesses 10 

Angle  covers  "        "       "     "        "  ««  13 

"     bars,  elements  of  even  legged 98 

"        "  "     uneven  legged 99 

"        "      moment  of  inertia 98,  99,  104 

•«        "     radius  of  gyration 98,  99,  104,  113 

"        "as  struts  and  tables  of  safe  loads 135-140 

"        "      acute  for  cable  roads 16 

"        "      approximate  rule  for  beams 69 

Areas  and  circumferences  of  circles 178-183 

Axles,  "Master  Car  Builder's  Standard " 15 

Beams,  explanation  of  tables  of  dimensions 1 

"      I,  dimensions  of  minimum  and  maximum  sizes 2 

"      I,  weights  of  various  web  thicknesses 3 

"      elements  of  I  section 92,  93 

"      moments  of  inertia 92-96,  105,  106 

"      radii  of  gyration 92-96,  105,  106,  113 

"      maximum  load  in  tons 90 

"      factors  of  safety 34 

"      greatest  safe  loads 35 

"      deflection  of 37 

"      limits  for  safe  load 33 

"         "      "   deflection 39 

"      table  of  safe  loads  and  deflections  for  1 40-45 

"      unsymmetrical  sections 34 

"      without  lateral  support 36,  73 

"      with  fixed  ends 38,  39 

"      continuous 38,  39,  75-77 

"      cantilever 38,  74-77 

"  iron  floor. .                                                                 . .52-55 


192  INDEX. 

Beams,  tables  of  safe  loads  and  spacing  for  floors 58-62 

"      approximate  rules  for  strength  of  various  sections. 68,  69 

"      bending  moments 78-81 

"      subject  to  both  bending  and  compression 84 

"      support,  brick  walls 65,  66 

"  "        irregular  loads 82,83 

Beam  sections  as  struts.     Tables  of  safe  loads 124-134 

Belting 175 

Bending  moments  for  beams 78-81 

"        resistance  of  iron  to 32 

Brick  arches  for  floors 54 

"      tie  rods  for 63 

"    walls,  beams  for  supporting 65,  66 

Bulb  plates 16 

"    iron • . . . (See  Deck  Beams.) 

Cantilever  beams 38,  74-77 

Channel  bars,  explanation  of  tables  of  dimensions 1 

"        "      dimensions  of  minimum  and  maximum  sec- 
tions        4 

"        "     weight  of  various  web  thicknesses «-, 

"         "      Car  Builder's  section 16 

"        "      elements  of 94,  95 

"        "     moments  of  inertia 94,  95,  105 

"        "      radii  of  gyration 94,  95,  105 

"        "      tables  of  safe  loads  and  deflections 46-49 

"        "      struts 121-122 

"        "      as  struts.     Tables  of  safe  loads 144-153 

"        "     approximate  rule  for  beams 69 

Circles,  areas  and  circumferences 178-183 

Columns  of  wrought  iron .154-159 

"      safe  loads  for  round 156, 157 

"       "square 158,159 

Compression,  wrought  iron  in 18-22 

Continuous  beams 38,  39,  75-77 

Cover  angles,  weight  per  yard  of  various  thicknesses 13 

Crane  stresses 163, 164 

Decimal  equivalents  for  fractions  of  an  inch 186 


INDEX.  193 

Deck  beams,  dimensions  of  minimum  and  maximum  sections      6 
"        «       weights  per  yard  of  various  web  thicknesses. . .       7 

"        "        elements  of 97-97 

"        "        moments  of  inertia 96,  97,  106 

"        "       radii  of  gyration 96,97,106 

"        "       formula  for  resistance  to  bending 35 

'        "        tables  of  safe  loads  and  deflections 50,  51 

"        "  "      "     "       "     and  spacing  for  floor 

beams 56,  57 

"        u       approximate  rule  for  beams 69 

Deflection  of  iron  beams 37 

"steel     "      27 

"        limits  of,  for  beams 39 

"        tables  of,  for  I  beams 40-45 

"  "       "     "    channel  bars.. 46-49 

"  "      "     "    deck  beams 50,51 

for  beams .' 78-81 

of  shafting 173 

Elasticity  of  wrought  iron 19-22 

Elements  of  structural  shapes 87-91 

"          "  "  "      tables ..92-101 

Factors  of  safety  for  beams 34 

"      "        "      "  struts 116-117 

"      "        '«       "  shafting 171 

Flat  bar  iron,  widths  and  thicknesses 14 

"     "       "      approximate  rule  for  beams  of 63 

Flexure (See  Deflection.) 

Floor  Beams 52-55 

"         "      rule  for  weights  of 53 

"        "      spacing  of 54 

"         ' '      lateral  strength 63 

Formulae  for  unsymmetrical  beams 35 

' '        approximate,  for  rolled  beams 67 

"        tables  of,  for  beams  of  various  sections 68,  69 

Fractions  of  an  inch  expressed  in  decimals 186 

Girder  stresses 165-166 

Gyration,  radius  of 87-88 


194 


INDEX. 


Gyration,  radius  of,  for  various  sections 92-101 

"  "     formulae  for  various  sections 102-111 

"    tables  112,113 

"    for  round  columns 155 

"  "      "  square        "       155 

Half-round  bar  iron,  sizes 14 

Horse-power  of  shafting 173 

I  beams (See  Beams  ) 

Inertia,  moments  of 87-88 

"  "          "  tables  for  various  sections 92-101 

"  "         "  formulae  for  various  sections 102-111 

"  "         "  for  combined  sections 108-111 

Iron,  ' <  Pencoyd  High  Test " 15 

"    "Pencoyd  Refined" 15 

"    strength  of  wrought 17 

"    ductility  of 17 

"    resistance  to  compression 18 

"    elasticity  of  rolled 19 

"    tensile  and  compressive  tests 20-22 

"    resistance  to  shearing 23 

"torsion 23 

"          "          "  bending 32 

"    columns 154-159 

"    shafting , 170-175 

"   struts 114-159 

"    sizes  of  bars ' 14 

"    weight  per  lineal  foot  of  bars 184-185 

Lateral  strength  of  floor  beams 63 

"      support,  beams  without 36,  73 

Latticing  for  channel  struts 121, 144-149 

Loads (See  Safe  Loads.) 

Modulus  of  elasticity  of  rolled  iron .19-22,  89 

•  <      «        «          "steel 26,27 

"      "  resistance  for  steel 26,  27 

"       ' '  rupture  for  rolled  iron 32 

Pins  and  rivets. .  ...  .160-162 


INDEX.  195 

Bails,  miner's  track 16 

"      splice  bar  for  do.  do 16 

'  *      for  slot  of  cable  roads 16 

Rivets  and  pins 160-1(52 

Roof  stresses 167-169 

Round  bar  iron,  sizes 14 

"      "      "      approximate  rule  for  beams  of 68 

Rule  for  weight  of  rolled  iron 15,  68 

"     "        "      "  iron  in  floor  beams 53 

"     "        thrust  of  brick  arches 63 

"     "        lateral  strength  of  I  beams 63,  64 

"     "  <«  "        "  channel  bars 63,64 

"     "        beams  bearing  irregular  loads 82 

Rules,  approximate  for  moments  of  inertia 107 

"    for  shafting ..170-175 

Safe  load,  co-efficient  for 88 

"    loads,  limits  of.  for  beams 33 

"        "      greatest,  for  beams 35 

"  "         "  I  beams 40-45 

"deckbeams 50-51 

"  "         "  channel  bars 46-49 

"        "      for  iron  struts  of  any  section 119 

"        "        "    "       "     tables  of,  for  beams,  channels, 

angles  and  tee  sections 123-159 

"        "      for  columns 156-159 

Shafting,  wrought  iron 170-175 

"       tables  of  diameters  and  lengths 176, 177 

Shearing  strength  of  wrought  iron 23 

Slot  rail  for  cable  roads 16 

Spacing  of  floor  beams 54 

"         "       "        "      tables  of,  for  eyebeam  sections. . .  .58-62 
"        "      "        "        "        "     "   deck  beam  sections..  56-57 

Specific  gravity — iron  and  steel 30 

Splice  bars  for  miner's  track  rail 16 

Square  bar  iron,  sizes 14 

"     root  angles,  weights  per  yard  of  various  thicknesses.     10 

Steel,  tensile  strength 24-26 

"      compressive  strength 24-26 

«'      transverse          "  ..27-28 


196  INDEX. 

Steel,  deflections  of  beams 27 

"    modulus  of  elasticity 27 

"    beams 93 

"    shafting 29 

"    struts 29,  HO,  123 

Stresses  in  framed  structures 163-169 

Structural  steel 24 

Struts  of  rolled  iron. 114  159 

"      steel 29,50,123 

"       factors  of  safety  for 116,  117 

"       table  of  ultimate  resistance  for  iron 118 

"       greatest  safe  loads  for  iron  of  any  section 119 

"       tables  of  safe  loads  for  beam  sections 124-134 

"  "      "      "        "         angle        "        138-140 

"          '"      "      "        *•        tee  "         142-143 

"  "      "      "        "         channel  sections 144-153 

Tee  bars,  explanation  of  tables  of  dimensions 1 

"     "      weights  and  dimensions  of  even- legged 11 

"     "          "        "  "  "  uneven-legged 13 

"     "      elements  of  even-legged 100 

"     "  *'        *'  uneven-legged 101 

"     "-     moments  of  inertia 100,101,104 

*'     "      radii  of  gyration 100,  101,  104 

"     "      as  struts  and  tables  of  safe  loads 141-143 

"     "      approximate  rule  for  beams. 69 

Tension  in  wrought  iron 17-22 

Tie  rods  for  brick  arches 63 

Torsional  strength  of  wrought  iron 23 

Ultimate  loads  for  iron  struts 118 

"          "       "steel       «'     31 

"       resistance  of  iron  to  bending  stress 32 

Weight  per  lineal  foot  of  round  and  square  iron 184 

"        "      "        "    "flat  iron 185 

Weight  of  cast  iron  separators 187 

bolts  and  nuts 188-189 

"         rivets . .  .190 


PENEDYD  SHAPES 


Plate  1 
Plates  2  tn2B  Scaled  Size 


Plate   Nn.  I 


Nn.l 
Wt.  2DD    to    233    Lbs, 


Nn.  2 
Wt.  143  to  2DI    Lhs. 

¥~^^ 


All  weights  ^iven  in  pounds  perYard. 


Plate   Nn.  2 


Wt.  IBB    tn     134    Lhs. 


weights  £ivEn  in   pounds  peirYard. 


PlatE   Nn. 


Alt  weights  £iven  in  pounds  perYard. 
Wi.   134:.  tn    IBl.lbs. 


ti* 


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-5V,- 
NQ.  S 


Plate   Na-4- 


Wt.BH.tn  l.U9.Lhs. 


Na.Sl 


Na.  B 


No.  22 
Wt.17  taZZLbs, 

*~    *  >3$: 


All  weights  £iven  in  pounds  perYard. 


Plate  Nn.  .5 


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S 


Nn.7 


Wt.  BD    to   !D6Lbs. 


H? 


Nn.  B 
All  weights  £iven  in   pounds  perYard. 


-;vW- 

..*! 


Plate   Nc.  B 


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pp 


Nn.!7 


Na.  IB 


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ND.  a 


05 


N  D.  I  D 


All  weights  ^iven  in   pounds   perYard. 


Plate   Ha.  7 


Wt..5d  tn  B3  Lhs.  Wt.  4D  to  E3  Lhs. 


NnlS 


* 


Nn.lB 


< 3% -—         <- 3*-~ -> 

Wt.Bl  tn  IDB.3  Lbs:         Wl.'BS  tn    75    Lhs. 


Nn.ll 


& 


00 


N  a.  1  2 


All  weights  ^iven  in   pounds  pet:  Yard. 


Flats   Nn.  B 


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WtBS    to    BB  Lbs. 


Wt.Sl    to    BB  Lbs, 


Nn.13  NaZD 

Wt.  28  ta  38  Lbs,        Wt-IS.S  tp  2I.S  Lbs. 


-sty 


All  weights  ^iven  in   pounds  pei:Yard. 


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ND.  3D 


h 


Nn.33 


in 

in 

J3 

a 
LG 


All  weights  ^iven  in   pounds  perYard. 


Plate   Nn.  ID 


No.  32 


Nn.3I 


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Plate  No.  I! 


All  weights  ^iven  in  pounds  perYard. 


'3  2 


Plate   No.  12 


Nn.  36 


Nn.  37 


B  I 


Nn.    38 

Wt.  43    tn    BD.5  Lbs, 


Nn.  3  3 
Wt.  3D    tn    54   Lhs. 


ff 


All  weights  ^iven  in  pounds  perYard. 


Plate   Nn.13 


Plate   Nn. 


2 


All  weights  £iven  in   pounds   perYard. 


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All  weights  £iven  in   pounds   perYard. 


Plate  Na.lB 


Na.E4 


No.ES 


m 


ra 


No,  B7 


"in 


DJ 


No.GB 
3% 


All  weights  ^iven  in   pounds   perYard. 


Plate   NQ.  17 


Wt.3.fi.5  Lbs. 
4" 


Wt.3    Lbs. 


No.7D 

Wt.3  Lbs. 


* 


No.71 


Wt.  ZE.Lbs. 
$>.... 


ND.BI 


Wt.ia.5  Lhs. 

'-,--  -2% 


1%'~»~ 


Nn.72 


ND.BD 


Na.73 


Wt.17.  52  Lhs.  Wt.B  Lhs.  Wt.11.7S  Us. 


«-      "5 


Nn.75 


Wt.IZ  Lhs.  Wt.7.I  Lhs. 


NnJB 


NnJB 


Wt.lD.S  Lbs. 

o» 


Nn.77 


All  weights  &\ven  in  pounds  perYard. 


Plate   Nn.  IB 


Wt.  ZZ-.E  Lbs. 

~    r^n 

'     *I     *•  "  ! 


ND.B3 


Wt.19.3  Lbs. 


Na.BZ 


All  weights  ^iven  in  pounds  perYard. 


Plate   Nn.lS 


Wt.  44.  I  Lhs. 


Wt.2D..4Lfas. 


IS/' 

3**V 


Np.lDY 

^ 


tv _, 

Wt.    48,^44  Lbs, 

I          ^          .  fc*     J 

xr-  %  -  ,-— 


Nn 


.IDE 


Wt.11.2  Lbs, 


J* 


•^•1 


Nn.9B 


Wt.2&.2SLhs. 


Na.37 


Wt.23.7S  Lhs. 


Wt.lB.7SLhs. 


Wt.  21.  Lhs. 

-------  2%-- 


Nn.lD4 


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All  weights  ^iven  in   pounds  perYard. 


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Wt.4LB  Lhs. 


Nn.an 

Wt.7  Lhs. 


Wt.3.1  Lhs. 


Wt.  3D.  7  Lhs.. 


Wt.B;7SLhs. 
Nn.92         <_  ......  -2'  .....  --> 


Wt.  33.  Lhs. 

-----     J* 


Nn.lD3 


Wt.25.H  Lhs. 


No.  94 


Wt.ZS.ZS  Lhs. 


Nn.95 


i_._.£J 
All  weights  £ivEn  in   pounds  perYard. 


Pi  ate   No.  21 


Wt.38.5    Lhs. 
--4' 


Wt.ZD.B   Lbs. 

15*4 


Nn.lll 


No.ina 

Wt.  17.7   Lbs. 


All  weights  ^iven  in   pounds  perYard. 


Plate   Nn.ZS 


Na.l2Q 


No.  129 


Na.132 


•^L\ 


AH  weights  ^iven  in   pounds   perYard. 


Plate   Nn.23 


Nal54 


•Nn.152 


No.l4D 


NfclSt 


Na.153 


Na.  141 


Na.142 


Ka.143 

All  weights  ^iven  in  pounds  perYard. 


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ND.I5S 


Nn.lSB 


Nn.I57 


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Plate   ND. 


NQ.IHD 


Nn.171 
Alt  weights  £ivEn  in   pounds   perYard. 


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All  weights  ^iven  in  paunds  perYard. 


Plate   No.  2  7 


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Nn.190  Wt.ZS  Lbs, 


Wt.SB  L-hs     '     No.  192 


No.  134. 


Nn.lB3. 


••*• 


Wt.4.3  Lhs.p.  Y2rd.  Wt  4.3  Lhs.  p. Yard. 


Nn  135     5 


ND.  me 

Nn.  197 


No.  19B 


'     2D,a  tn  34.5  Lbs. 


All  weights  ^iven  in   pounds  perYard. 


Plate   No.  28 


METHOD  OF  INCREASING 
SECTIONAL  AREAS. 


Cross-hatched  portions  represent 

the  minimum  sections, and  the 

blank  portions  the  added  areas. 


W, 


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